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Open Journal of Discrete Applied Mathematics最新文献

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Some basic properties of Sombor indices Sombor指数的一些基本性质
Open Journal of Discrete Applied Mathematics Pub Date : 2021-01-09 DOI: 10.30538/psrp-odam2021.0047
I. Gutman
{"title":"Some basic properties of Sombor indices","authors":"I. Gutman","doi":"10.30538/psrp-odam2021.0047","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0047","url":null,"abstract":"The recently introduced class of vertex-degree-based molecular structure descriptors, called Sombor indices ((SO)), are examined and a few of their basic properties established. Simple lower and upper bounds for (SO) are determined. It is shown that any vertex-degree-based descriptor can be viewed as a special case of a Sombor-type index.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116666500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 72
Degree affinity number of certain (2)-regular graphs 某些(2) -正则图的度亲和数
Open Journal of Discrete Applied Mathematics Pub Date : 2020-12-14 DOI: 10.30538/psrp-odam2020.0046
J. Kok
{"title":"Degree affinity number of certain (2)-regular graphs","authors":"J. Kok","doi":"10.30538/psrp-odam2020.0046","DOIUrl":"https://doi.org/10.30538/psrp-odam2020.0046","url":null,"abstract":"This paper furthers the study on a new graph parameter called the degree affinity number. The degree affinity number of a graph (G) is obtained by iteratively constructing graphs, (G_1,G_2,dots,G_k) of increased size by adding a maximal number of edges between distinct pairs of distinct vertices of equal degree. Preliminary results for certain (2)-regular graphs are presented.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133707952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deutsch paths and their enumeration 德语路径及其列举
Open Journal of Discrete Applied Mathematics Pub Date : 2020-03-04 DOI: 10.30538/psrp-odam2021.0049
H. Prodinger
{"title":"Deutsch paths and their enumeration","authors":"H. Prodinger","doi":"10.30538/psrp-odam2021.0049","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0049","url":null,"abstract":"A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125541930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Kolakoski sequence: links between recurrence, symmetry and limit density Kolakoski序列:递归、对称和极限密度之间的联系
Open Journal of Discrete Applied Mathematics Pub Date : 2020-02-19 DOI: 10.30538/psrp-odam2021.0052
A. D. Corte
{"title":"Kolakoski sequence: links between recurrence, symmetry and limit density","authors":"A. D. Corte","doi":"10.30538/psrp-odam2021.0052","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0052","url":null,"abstract":"The Kolakoski sequence $S$ is the unique element of (leftlbrace 1,2 rightrbrace^{omega}) starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of (S) as a unifying tool to address the links between the main open questions - recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is (frac{1}{2}).","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"46 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117310037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A new recursion for Bressoud’s polynomials 布雷苏德多项式的一种新递归
Open Journal of Discrete Applied Mathematics Pub Date : 2020-01-15 DOI: 10.30538/psrp-odam2020.0034
H. Prodinger
{"title":"A new recursion for Bressoud’s polynomials","authors":"H. Prodinger","doi":"10.30538/psrp-odam2020.0034","DOIUrl":"https://doi.org/10.30538/psrp-odam2020.0034","url":null,"abstract":"A new recursion in only one variable allows very simple verifications of Bressoud's polynomial identities, which lead to the Rogers-Ramanujan identities. This approach might be compared with an earlier approach due to Chapman. Applying the $q$-Chu-Vandermonde convolution, as suggested by Cigler, makes the computations particularly simple and elementary. The same treatment is also applied to the Santos polynomials and perhaps more polynomials from a list of Rogers-Ramanujan like polynomials cite{Sills}.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125589744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The smallest sum-connectivity index on trees with n vertices and k pendant vertices 在有n个顶点和k个垂顶点的树上的最小和连通性指数
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-31 DOI: 10.30538/PSRP-ODAM2019.0013
Yuedan Yao
{"title":"The smallest sum-connectivity index on trees with n vertices and k pendant vertices","authors":"Yuedan Yao","doi":"10.30538/PSRP-ODAM2019.0013","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0013","url":null,"abstract":"For a given connected graph G and a real number α, denote by d(u) the degree of vertex u of G, and denote by χα(G) = ∑uv∈E(G) ( d(u) + d(v) )α the general sum-connectivity index of G. In the present note, we determine the smallest general sum-connectivity index of trees (resp., chemical trees) together with corresponding extremal trees among all trees (resp., chemical trees) with n vertices and k pendant vertices for 0 < α < 1.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124189372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Computing multiplicative topological indices of some chemical nenotubes and networks 计算一些化学纳米管和网络的乘法拓扑指数
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-31 DOI: 10.30538/psrp-odam2019.0018
Zaryab Hussain, Ahsan Ahsan, S. H. Arshad
{"title":"Computing multiplicative topological indices of some chemical nenotubes and networks","authors":"Zaryab Hussain, Ahsan Ahsan, S. H. Arshad","doi":"10.30538/psrp-odam2019.0018","DOIUrl":"https://doi.org/10.30538/psrp-odam2019.0018","url":null,"abstract":"Zaryab Hussain1,2,∗, Ahsan3 and Shahid Hussain Arshad4 1 Department of Mathematics, Punjab College of Commerce New Campus Faisalabad Pakistan. 2 Department of Mathematics, Government College University Faisalabad Pakistan. 3 Superior Group of Colleges Faisalabad Campus, Faisalabad Pakistan.; ahsanulhaq8006@gmail.com 4 Department of Applied Sciences, National Textile University Faisalabad Pakistan.; shahidarshad@ntu.edu.pk * Correspondence: zaryabhussain2139@gmail.com; Tel.: +923207488346","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"141 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124567491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
M-polynomial of some cactus chains and their topological indices 仙人掌链的m -多项式及其拓扑指标
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-31 DOI: 10.30538/PSRP-ODAM2019.0016
B. Basavanagoud, Anand P. Barangi
{"title":"M-polynomial of some cactus chains and their topological indices","authors":"B. Basavanagoud, Anand P. Barangi","doi":"10.30538/PSRP-ODAM2019.0016","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2019.0016","url":null,"abstract":"T he concept of degree is analogous to the concept of valence in organic chemistry with a limitation that degree of any vertex in any chemical graph is at most 4. This gives graph theory a broad way to chemistry. It is always interesting to find some properties of graphs or molecular graphs which are invariant. Topological indices and polynomials are foremost among them. Over the last decade there are numerous research papers devoted to topological indices and polynomials. Several topological indices have been defined in the literature. For various topological indices one can refer to [1–8]. Let G = (V, E) be a simple, undirected graph. Let V(G) be the vertex set and E(G) be the edge set of the graph G, respectively. The degree dG(v) of a vertex v ∈ V(G) is the number of edges incident to it in G. Let {v1, v2, ..., vn} be the vertices of G and let di = dG(vi). A graph G is said to be r− regular if degree of each vertex in G is r. A graph is called cycle if it is 2− regular. A cactus graph is a connected graph in which any two simple cycles have at most one vertex in common. Every cycle of cactus graph is chordless and every block of a cactus graph is either an edge or a cycle. If all blocks of a cactus graph are triangular then it is called triangular cacti. If all the triangles of a triangular cactus graph has at most two cut-vertices and each cut-vertex is shared by exactly two triangles then we say that triangular cactus graph is a chain triangular cactus. In chain triangular cactus if we replace triangles by cycles of length 4 then we obtain cacti whose every block is C4, such cacti are called square cacti. For ortho-chain square cactus the cut vertices are adjacent and a para-chain square cactus their cut vertices are not adjacent. Recent study on some cactus chain can be found in [9–11] and references cited therein. For undefined graph theoretic terminology used in this paper can be found in [12]. The general form of degree-based topological index of a graph is given by","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126189578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Wiener index of uniform hypergraphs induced by trees 树诱导一致超图的Wiener指数
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-31 DOI: 10.30538/psrp-odam2019.0019
A. Dobrynin
{"title":"Wiener index of uniform hypergraphs induced by trees","authors":"A. Dobrynin","doi":"10.30538/psrp-odam2019.0019","DOIUrl":"https://doi.org/10.30538/psrp-odam2019.0019","url":null,"abstract":"The Wiener index W(G) of a graph G is defined as the sum of distances between its vertices. A tree T generates r-uniform hypergraph Hr,k(T) by the following way: hyperedges of cardinality r correspond to edges of the tree and adjacent hyperedges have k vertices in common. A relation between quantities W(T) and W(Hr,k(T)) is established.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127495710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A comparative analysis of the travelling salesman problem: Exact and machine learning techniques 旅行推销员问题的比较分析:精确和机器学习技术
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-31 DOI: 10.30538/psrp-odam2019.0020
Jeremiah Ishaya, A. Ibrahim, Nassirou Lo
{"title":"A comparative analysis of the travelling salesman problem: Exact and machine learning techniques","authors":"Jeremiah Ishaya, A. Ibrahim, Nassirou Lo","doi":"10.30538/psrp-odam2019.0020","DOIUrl":"https://doi.org/10.30538/psrp-odam2019.0020","url":null,"abstract":"Given a set of locations or cities and the cost of travel between each location, the task is to find the optimal tour that will visit each locations exactly once and return to the starting location. We solved a routing problem with focus on Travelling Salesman Problem using two algorithms. The task of choosing the algorithm that gives optimal result is difficult to accomplish in practice. However, most of the traditional methods are computationally bulky and with the rise of machine learning algorithms, which gives a near optimal solution. This paper studied two methods: branch-and-cut and machine learning methods. In the machine learning method, we used neural networks and reinforcement learning with 2-opt to train a recurrent network that predict a distribution of different location permutations using the negative tour-length as the reward signal and policy gradient to optimize the parameters of recurrent network. The improved machine learning with 2-opt give near-optimal results on 2D Euclidean with upto 200 nodes.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"368 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121659333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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