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Open Journal of Discrete Applied Mathematics最新文献

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Minimal graphs for hamiltonian extension 哈密顿扩展的最小图
Open Journal of Discrete Applied Mathematics Pub Date : 2019-12-10 DOI: 10.30538/psrp-odam2020.0026
C. Picouleau
{"title":"Minimal graphs for hamiltonian extension","authors":"C. Picouleau","doi":"10.30538/psrp-odam2020.0026","DOIUrl":"https://doi.org/10.30538/psrp-odam2020.0026","url":null,"abstract":"For every $nge 3$ we determine the minimum number of edges of graph with $n$ vertices such that for any non edge $xy$ there exits a hamiltonian cycle containing $xy$.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130591316","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
Reinterpreting the middle-levels theorem via natural enumeration of ordered trees 通过有序树的自然枚举重新解释中层定理
Open Journal of Discrete Applied Mathematics Pub Date : 2019-11-01 DOI: 10.30538/psrp-odam2020.0033
I. Dejter
{"title":"Reinterpreting the middle-levels theorem via natural enumeration of ordered trees","authors":"I. Dejter","doi":"10.30538/psrp-odam2020.0033","DOIUrl":"https://doi.org/10.30538/psrp-odam2020.0033","url":null,"abstract":"Let $0<kinmathbb{Z}$. A reinterpretation of the proof of existence of Hamilton cycles in the middle-levels graph $M_k$ induced by the vertices of the $(2k+1)$-cube representing the $k$- and $(k+1)$-subsets of ${0,ldots,2k}$ is given via an associated dihedral quotient graph of $M_k$ whose vertices represent the ordered (rooted) trees of order $k+1$ and size $k$.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116485747","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: 13
The Hadamard product and recursively defined sequences Hadamard积和递归定义的序列
Open Journal of Discrete Applied Mathematics Pub Date : 2019-02-22 DOI: 10.30538/psrp-odam2020.0025
Sergei Kazenas
{"title":"The Hadamard product and recursively defined sequences","authors":"Sergei Kazenas","doi":"10.30538/psrp-odam2020.0025","DOIUrl":"https://doi.org/10.30538/psrp-odam2020.0025","url":null,"abstract":"In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some formulas for the solutions of linear difference equations with variable coefficients are obtained. At the end of the paper, some integer sequences associated with a quadratic map are considered.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114674828","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: 4
Characterizing Trees with Minimal ABC Index with Computer Search: A Short Survey 用计算机搜索刻画具有最小ABC索引的树:一个简短的调查
Open Journal of Discrete Applied Mathematics Pub Date : 2018-12-30 DOI: 10.30538/PSRP-ODAM2018.0005
Yiming Zheng, Wenshui Lin, Qi'an Chen, Linshan Huang, Zhixi Wu, Xiamen China Computing for Smart City
{"title":"Characterizing Trees with Minimal ABC Index with Computer Search: A Short Survey","authors":"Yiming Zheng, Wenshui Lin, Qi'an Chen, Linshan Huang, Zhixi Wu, Xiamen China Computing for Smart City","doi":"10.30538/PSRP-ODAM2018.0005","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2018.0005","url":null,"abstract":"The atom-bond connectivity (ABC ) index of a graph G = (V, E) is defined as ABC(G) = ∑","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129539781","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: 8
Path Decomposition Number of Certain Graphs 若干图的路径分解数
Open Journal of Discrete Applied Mathematics Pub Date : 2018-12-30 DOI: 10.30538/PSRP-ODAM2018.0004
O. Oyewumi, A. Akwu, Theresa Iveren Azer
{"title":"Path Decomposition Number of Certain Graphs","authors":"O. Oyewumi, A. Akwu, Theresa Iveren Azer","doi":"10.30538/PSRP-ODAM2018.0004","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2018.0004","url":null,"abstract":"Let G be a simple, finite and connected graph. A graph is said to be decomposed into subgraphs H1 and H2 which is denoted by G = H1 ⊕H2, if G is the edge disjoint union of H1 and H2. Assume that G = H1 ⊕ H2 ⊕ · · · ⊕ Hk and if each Hi, 1 ≤ i ≤ k, is a path or cycle in G, then the collection of edge-disjoint subgraphs of G denoted by ψ is called a path decomposition of G. If each Hi is a path in G then ψ is called an acyclic path decomposition of G. The minimum cardinality of a path decomposition of G, denoted by π(G), is called the path decomposition number and the minimum cardinality of an acyclic path decomposition of G, denoted by πa(G), is called the acyclic path decomposition number of G. In this paper, we determine path decomposition number for a number of graphs in particular, the Cartesian product of graphs. We also provided bounds for π(G) and πa(G) for these graphs. Mathematics Subject Classification: 05C70.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123560845","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: 3
A Note on the Zeroth-order General Randić Index of Polygonal Cacti 关于多边形仙人掌的零阶一般randiki指数的注记
Open Journal of Discrete Applied Mathematics Pub Date : 2018-12-30 DOI: 10.30538/PSRP-ODAM2018.0001
Jiachang Ye, Yuedan Yao
{"title":"A Note on the Zeroth-order General Randić Index of Polygonal Cacti","authors":"Jiachang Ye, Yuedan Yao","doi":"10.30538/PSRP-ODAM2018.0001","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2018.0001","url":null,"abstract":"The zeroth-order general Randić index of a simple connected graph G is defined as Rα(G) = ∑ u∈V (G) ( d(u) )α , where d(u) is the degree of u and α 6∈ {0, 1} is a real number. A k-polygonal cactus is a connected graph in which every edge lies in exactly one cycle of length k. In this paper, we present the extremal k-polygonal cactus with n cycles for k ≥ 3 with respect to the zeroth-order general Randić index. Mathematics Subject Classification: Primary: 05C15; Secondary: 05C12.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128574293","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
Zero-Sum Flow Number of Some Grid Graphs 一些网格图的零和流数
Open Journal of Discrete Applied Mathematics Pub Date : 2018-12-30 DOI: 10.30538/psrp-odam2018.0003
M. K. Siddiqui, M. Naeem, M. Imran
{"title":"Zero-Sum Flow Number of Some Grid Graphs","authors":"M. K. Siddiqui, M. Naeem, M. Imran","doi":"10.30538/psrp-odam2018.0003","DOIUrl":"https://doi.org/10.30538/psrp-odam2018.0003","url":null,"abstract":"For an undirected graph G, a zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident to each vertex is zero, and we call it a zero-sum k-flow if the absolute values of edges are less than k. We define the zero-sum flow number of G as the least integer k for which G admits a zero sum k-flow. In this paper we have given complete zero-sum flow and zero sum number for octagonal grid, generalized prism and book graph. Mathematics Subject Classification: Primary: 05C21; Secondary: 05C50.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132120276","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
Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs 正则图的度减法邻接特征值与能量
Open Journal of Discrete Applied Mathematics Pub Date : 2018-12-30 DOI: 10.30538/PSRP-ODAM2018.0002
H. Ramane, Hemaraddi N. Maraddi
{"title":"Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs","authors":"H. Ramane, Hemaraddi N. Maraddi","doi":"10.30538/PSRP-ODAM2018.0002","DOIUrl":"https://doi.org/10.30538/PSRP-ODAM2018.0002","url":null,"abstract":"Let V (G) = {v1, v2, . . . , vn} be the vertex set of G and let dG(vi) be the degree of a vertex vi in G. The degree subtraction adjacency matrix of G is a square matrix DSA(G) = [dij ], in which dij = dG(vi) − dG(vj), if vi is adjacent to vj and dij = 0, otherwise. In this paper we express the eigenvalues of the degree subtraction adjacency matrix of subdivision graph, semitotal point graph, semitotal line graph and total graph of a regular graph in terms of the adjacency eigenvalues of G. Further we obtain the degree subtraction adjacency energy of these graphs. Mathematics Subject Classification: Primary: 05C50; Secondary: 05C07.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"28 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116622958","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
On graceful difference labelings of disjoint unions of circuits 关于回路不相交并的优美差分标记
Open Journal of Discrete Applied Mathematics Pub Date : 2018-08-01 DOI: 10.30538/psrp-odam2019.0021
A. Hertz, C. Picouleau
{"title":"On graceful difference labelings of disjoint unions of circuits","authors":"A. Hertz, C. Picouleau","doi":"10.30538/psrp-odam2019.0021","DOIUrl":"https://doi.org/10.30538/psrp-odam2019.0021","url":null,"abstract":"A graceful difference labeling (gdl for short) of a directed graph G with vertex set V is a bijection f between V and {1,...,|V|} such that, when each arc uv is assigned the difference label f(v)-f(u), the resulting arc labels are distinct. We conjecture that all disjoint unions of circuits have a gdl, except in two particular cases. We prove partial results which support this conjecture.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133064799","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
Graph energy and nullity 图能量和零
Open Journal of Discrete Applied Mathematics Pub Date : 1900-01-01 DOI: 10.30538/psrp-odam2021.0051
I. Gutman
{"title":"Graph energy and nullity","authors":"I. Gutman","doi":"10.30538/psrp-odam2021.0051","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0051","url":null,"abstract":"The energy of a graph is the sum of absolute values of its eigenvalues. The nullity of a graph is the algebraic multiplicity of number zero in its spectrum. Empirical facts indicate that graph energy decreases with increasing nullity, but proving this property is difficult. In this paper, a method is elaborated by means of which the effect of nullity on graph energy can be quantitatively estimated.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115320535","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: 4
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