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Open Journal of Discrete Applied Mathematics最新文献

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Sombor indices–back to geometry Sombor指数——回到几何
Open Journal of Discrete Applied Mathematics Pub Date : 2022-07-23 DOI: 10.30538/psrp-odam2022.0072
I. Gutman
{"title":"Sombor indices–back to geometry","authors":"I. Gutman","doi":"10.30538/psrp-odam2022.0072","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0072","url":null,"abstract":"The Sombor index ((SO)) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of (sqrt{d_i^2+d_j^2}), where (d_i) is the degree of the (i)-th vertex. It has been conceived using geometric considerations. Numerous researches of (SO) that followed, ignored its geometric origin. We now show that geometry-based reasonings reveal the geometric background of several classical topological indices (Zagreb, Albertson) and lead to a series of new (SO)-like degree-based graph invariants.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126359874","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: 9
Note: Vertex stress in generalized Johnson graphs of diameter 2 注:直径为2的广义Johnson图的顶点应力
Open Journal of Discrete Applied Mathematics Pub Date : 2022-07-23 DOI: 10.30538/psrp-odam2022.0073
J. Kok
{"title":"Note: Vertex stress in generalized Johnson graphs of diameter 2","authors":"J. Kok","doi":"10.30538/psrp-odam2022.0073","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0073","url":null,"abstract":"This note establishes the induced vertex stress, total induced vertex stress, vertex stress and total vertex stress of the generalized Johnson graphs of diameter (2). The note serves as the foundation to establish the same parameters for generalized Johnson graphs of diameter greater than or equal to (3).","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131310931","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
Bijections of (k)-plane trees (k) -梧桐树的双射
Open Journal of Discrete Applied Mathematics Pub Date : 2022-04-30 DOI: 10.30538/psrp-odam2022.0068
I. Okoth
{"title":"Bijections of (k)-plane trees","authors":"I. Okoth","doi":"10.30538/psrp-odam2022.0068","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0068","url":null,"abstract":"A (k)-plane tree is a tree drawn in the plane such that the vertices are labeled by integers in the set ({1,2,ldots,k}), the children of all vertices are ordered, and if ((i,j)) is an edge in the tree, where (i) and (j) are labels of adjacent vertices in the tree, then (i+jleq k+1). In this paper, we construct bijections between these trees and the sets of (k)-noncrossing increasing trees, locally oriented ((k-1))-noncrossing trees, Dyck paths, and some restricted lattice paths.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130410528","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
A note on marginal entropy of graphs 关于图的边际熵的注记
Open Journal of Discrete Applied Mathematics Pub Date : 2022-04-30 DOI: 10.30538/psrp-odam2022.0071
Ting Zhou, Zhen Lin, L. Miao
{"title":"A note on marginal entropy of graphs","authors":"Ting Zhou, Zhen Lin, L. Miao","doi":"10.30538/psrp-odam2022.0071","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0071","url":null,"abstract":"In 2006, Konstantinova proposed the marginal entropy of a graph based on the Wiener index. In this paper, we obtain the marginal entropy of the complete multipartite graphs, firefly graphs, lollipop graphs, clique-chain graphs, Cartesian product and join of two graphs, which extends the results of Sahin.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128645054","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
Type-II generalized Pythagorean bipolar fuzzy soft sets and application for decision making 广义毕达哥拉双极模糊软集及其在决策中的应用
Open Journal of Discrete Applied Mathematics Pub Date : 2022-04-30 DOI: 10.30538/psrp-odam2022.0069
M. Palanikumar, K. Arulmozhi
{"title":"Type-II generalized Pythagorean bipolar fuzzy soft sets and application for decision making","authors":"M. Palanikumar, K. Arulmozhi","doi":"10.30538/psrp-odam2022.0069","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0069","url":null,"abstract":"In the present communication, we introduce the theory of Type-II generalized Pythagorean bipolar fuzzy soft sets and define complementation, union, intersection, AND, and OR. The Type-II generalized Pythagorean bipolar fuzzy soft sets are presented as a generalization of soft sets. We showed De Morgan's laws, associate laws, and distributive laws in Type-II generalized Pythagorean bipolar fuzzy soft set theory. Also, we advocate an algorithm to solve the decision-making problem based on a soft set model.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127305839","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
Lucky (k)-polynomials of null and complete split graphs Lucky (k) - null和完全分割图的多项式
Open Journal of Discrete Applied Mathematics Pub Date : 2022-04-30 DOI: 10.30538/psrp-odam2022.0070
J. Kok
{"title":"Lucky (k)-polynomials of null and complete split graphs","authors":"J. Kok","doi":"10.30538/psrp-odam2022.0070","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0070","url":null,"abstract":"The concept of Lucky colorings of a graph is used to introduce the notion of the Lucky (k)-polynomials of null graphs. We then give the Lucky (k)-polynomials for complete split graphs and generalized star graphs. Finally, further problems of research related to this concept are discussed.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132154734","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
TEMO theorem for Sombor index Sombor指数的TEMO定理
Open Journal of Discrete Applied Mathematics Pub Date : 2022-04-10 DOI: 10.30538/psrp-odam2022.0067
I. Gutman
{"title":"TEMO theorem for Sombor index","authors":"I. Gutman","doi":"10.30538/psrp-odam2022.0067","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0067","url":null,"abstract":"TEMO = topological effect on molecular orbitals was discovered by Polansky and Zander in 1982, in connection with the eigenvalues of molecular graphs. Eventually, analogous regularities were established for a variety of other topological indices. We now show that a TEMO-type regularity also holds for the Sombor index ((SO)): For the graphs (S) and (T), constructed by connecting a pair of vertex-disjoint graphs by two edges, (SO(S) < SO(T)) holds. Analogous relations are verified for several other degree-based graph invariants.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127282970","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
A note on binomial transform of the generalized fifth order Jacobsthal numbers 广义五阶jacobthal数的二项式变换
Open Journal of Discrete Applied Mathematics Pub Date : 2022-03-16 DOI: 10.30538/psrp-odam2022.0066
Y. Soykan, E. Taşdemir, Vedat Irge
{"title":"A note on binomial transform of the generalized fifth order Jacobsthal numbers","authors":"Y. Soykan, E. Taşdemir, Vedat Irge","doi":"10.30538/psrp-odam2022.0066","DOIUrl":"https://doi.org/10.30538/psrp-odam2022.0066","url":null,"abstract":"In this paper, we define the binomial transform of the generalized fifth order Jacobsthal sequence and as special cases, the binomial transform of the fifth order Jacobsthal, fifth order Jacobsthal-Lucas, adjusted fifth order Jacobsthal and modified fifth order Jacobsthal-Lucas sequences will be introduced. We investigate their properties in details.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116660980","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
Qualitative analysis of solutions for a parabolic type Kirchhoff equation with logarithmic nonlinearity 具有对数非线性的抛物型Kirchhoff方程解的定性分析
Open Journal of Discrete Applied Mathematics Pub Date : 2021-12-31 DOI: 10.30538/psrp-odam2021.0054
E. Pişkin, Tuğrul Cömert
{"title":"Qualitative analysis of solutions for a parabolic type Kirchhoff equation with logarithmic nonlinearity","authors":"E. Pişkin, Tuğrul Cömert","doi":"10.30538/psrp-odam2021.0054","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0054","url":null,"abstract":"In this work, we investigate the initial boundary-value problem for a parabolic type Kirchhoff equation with logarithmic nonlinearity. We get the existence of global weak solution, by the potential wells method and energy method. Also, we get results of the decay and finite time blow up of the weak solutions.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125464648","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
The inverse sum indeg index ((ISI)) and (ISI) energy of Hyaluronic Acid-Paclitaxel molecules used in anticancer drugs 抗癌药物中使用的透明质酸-紫杉醇分子的逆和指数((ISI))和能量(ISI)
Open Journal of Discrete Applied Mathematics Pub Date : 2021-12-24 DOI: 10.30538/psrp-odam2021.0065
Özge Çolakoǧlu Havare
{"title":"The inverse sum indeg index ((ISI)) and (ISI) energy of Hyaluronic Acid-Paclitaxel molecules used in anticancer drugs","authors":"Özge Çolakoǧlu Havare","doi":"10.30538/psrp-odam2021.0065","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0065","url":null,"abstract":"The inverse sum indeg index (ISI(G)) of a graph is equal to the sum over all edges (uvin E(G)) of weights (frac{d_{u}d_{v}}{d_{u}+d_{v}}). In this paper, we calculated the inverse indeg indices and inverse indeg energies that give information about the physicochemical properties and biological characteristics of Hyaluronic Acid-Paclitaxel conjugates used in the production of drugs used in the treatment of cancer disease. This study presents the relation between the ISI index and the ISI energy of the molecular graph of Hyaluronic Acid-Paclitaxel conjugates.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115699738","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: 10
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