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Open Journal of Discrete Applied Mathematics最新文献

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Degree-based topological indices of product graphs 基于度的积图拓扑指标
Open Journal of Discrete Applied Mathematics Pub Date : 2021-11-01 DOI: 10.30538/psrp-odam2021.0064
Xiaojing Wang, Zhen Lin, L. Miao
{"title":"Degree-based topological indices of product graphs","authors":"Xiaojing Wang, Zhen Lin, L. Miao","doi":"10.30538/psrp-odam2021.0064","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0064","url":null,"abstract":"In this paper, we obtain the quantitative calculation formula of the degree-based topological indices of four standard products for the path and regular graphs, which unify to solve the question on the product of these basic graphs without dealing with it one by one separately. As applications, we give the corresponding calculation formula of the general Randić index, the first general Zagreb index, and the general sum-connectivity index.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133550169","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
On characteristic polynomial and energy of Sombor matrix Sombor矩阵的特征多项式与能量
Open Journal of Discrete Applied Mathematics Pub Date : 2021-10-31 DOI: 10.30538/psrp-odam2021.0062
Gowtham Kalkere Jayanna, I. Gutman
{"title":"On characteristic polynomial and energy of Sombor matrix","authors":"Gowtham Kalkere Jayanna, I. Gutman","doi":"10.30538/psrp-odam2021.0062","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0062","url":null,"abstract":"Let (G) be a simple graph with vertex set (V={v_1,v_2,ldots,v_n }), and let (d_i) be the degree of the vertex (v_i). The Sombor matrix of (G) is the square matrix (mathbf A_{SO}) of order (n), whose ((i,j))-element is (sqrt{d_i^2+d_j^2}) if (v_i) and (v_j) are adjacent, and zero otherwise. We study the characteristic polynomial, spectrum, and energy of (mathbf A_{SO}). A few results for the coefficients of the characteristic polynomial, and bounds for the energy of (mathbf A_{SO}) are established.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132571715","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: Characterization of star, helm, flower and complete graphs by total vertex stress 注:用总顶点应力描述星形图、盔形图、花形图和完全图
Open Journal of Discrete Applied Mathematics Pub Date : 2021-10-31 DOI: 10.30538/psrp-odam2021.0061
J. Kok
{"title":"A note: Characterization of star, helm, flower and complete graphs by total vertex stress","authors":"J. Kok","doi":"10.30538/psrp-odam2021.0061","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0061","url":null,"abstract":"This note presents the characterization of the families of star, helm, flower and complete graphs by total vertex stress. The note does not present results for many families of graphs but, it highlights important philosophical (math. phil.) aspects for further research. In particular the novelty concepts of forgiven contradictions denoted by, iff(_f) as well as iffness and (f)-statements are introduced. The author suggests that the characterization of other families of graphs by total vertex stress is possible.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131411684","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
The evolutionary spatial snowdrift game on a cycle: An asymptotic analysis 循环上的演化空间漂移博弈:渐近分析
Open Journal of Discrete Applied Mathematics Pub Date : 2021-10-31 DOI: 10.30538/psrp-odam2021.0063
Benedikt V. Meylahn, J. V. Vuuren
{"title":"The evolutionary spatial snowdrift game on a cycle: An asymptotic analysis","authors":"Benedikt V. Meylahn, J. V. Vuuren","doi":"10.30538/psrp-odam2021.0063","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0063","url":null,"abstract":"The temporal dynamics of games have been studied widely in evolutionary spatial game theory using simulation. Each player is usually represented by a vertex of a graph and plays a particular game against every adjacent player independently. These games result in payoffs to the players which affect their relative fitness. The fitness of a player, in turn, affects its ability to reproduce. In this paper, we analyse the temporal dynamics of the evolutionary 2-person, 2-strategy snowdrift game in which players are arranged along a cycle of arbitrary length. In this game, each player has the option of adopting one of two strategies, namely cooperation or defection, during each game round. We compute the probability of retaining persistent cooperation over time from a random initial assignment of strategies to players. We also establish bounds on the probability that a small number of players of a particular mutant strategy introduced randomly into a cycle of players which have established the opposite strategy leads to the situation where all players eventually adopt the mutant strategy. We adopt an analytic approach throughout as opposed to a simulation approach clarifying the underlying dynamics intrinsic to the entire class of evolutionary spatial snowdrift games.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127744025","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
Some new operators for Fermatean fuzzy matrices Fermatean模糊矩阵的一些新算子
Open Journal of Discrete Applied Mathematics Pub Date : 2021-10-06 DOI: 10.30538/psrp-odam2021.0060
I. Silambarasan
{"title":"Some new operators for Fermatean fuzzy matrices","authors":"I. Silambarasan","doi":"10.30538/psrp-odam2021.0060","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0060","url":null,"abstract":"In this paper, we define some new operators ([(A $ B),(A # B),(Aast B),(A rightarrow B) ]) of Fermatean fuzzy matrices and investigate their algebraic properties. Further, the necessity and possibility operators of Fermatean fuzzy matrices are proved. Finally, we have identified and proved several of these properties, particularly those involving the operator (Arightarrow B) defined as Fermatean fuzzy implication with other operators.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116727645","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
(S)-norms on anti (Q)-fuzzy subgroups (S)反(Q) -fuzzy子群上的-范数
Open Journal of Discrete Applied Mathematics Pub Date : 2021-10-06 DOI: 10.30538/psrp-odam2021.0059
R. Rasuli
{"title":"(S)-norms on anti (Q)-fuzzy subgroups","authors":"R. Rasuli","doi":"10.30538/psrp-odam2021.0059","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0059","url":null,"abstract":"In this paper, by using (S)-norms, we defined anti fuzzy subgroups and anti fuzzy normal subgroups which are new notions and considered their fundamental properties and also made an attempt to study the characterizations of them. Next we investigated image and pre image of them under group homomorphisms. Finally, we introduced the direct sum of them and proved that direct sum of any family of them is also anti fuzzy subgroups and anti fuzzy normal subgroups under (S)-norms, respectively.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"429 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122798439","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
Spectral conditions for the Bipancyclic Bipartite graphs 双环二部图的谱条件
Open Journal of Discrete Applied Mathematics Pub Date : 2021-06-25 DOI: 10.30538/psrp-odam2021.0058
Rao Li
{"title":"Spectral conditions for the Bipancyclic Bipartite graphs","authors":"Rao Li","doi":"10.30538/psrp-odam2021.0058","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0058","url":null,"abstract":"Let (G = (X, Y; E)) be a bipartite graph with two vertex partition subsets (X) and (Y). (G) is said to be balanced if (|X| = |Y|) and (G) is said to be bipancyclic if it contains cycles of every even length from (4) to (|V(G)|). In this note, we present spectral conditions for the bipancyclic bipartite graphs.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115287587","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
Nirmala energy 能量吧
Open Journal of Discrete Applied Mathematics Pub Date : 2021-06-25 DOI: 10.30538/psrp-odam2021.0055
I. Gutman, V. Kulli
{"title":"Nirmala energy","authors":"I. Gutman, V. Kulli","doi":"10.30538/psrp-odam2021.0055","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0055","url":null,"abstract":"A novel vertex-degree-based topological invariant, called Nirmala index, was recently put forward, defined as the sum of the terms (sqrt{d(u)+d(v)}) over all edges (uv) of the underlying graph, where (d(u)) is the degree of the vertex (u). Based on this index, we now introduce the respective ``Nirmala matrix'', and consider its spectrum and energy. An interesting finding is that some spectral properties of the Nirmala matrix, including its energy, are related to the first Zagreb index.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116508003","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
Possibility Pythagorean bipolar fuzzy soft sets and its application 可能性毕达哥拉斯双极模糊软集及其应用
Open Journal of Discrete Applied Mathematics Pub Date : 2021-06-25 DOI: 10.30538/psrp-odam2021.0056
M. Palanikumar, K. Arulmozhi
{"title":"Possibility Pythagorean bipolar fuzzy soft sets and its application","authors":"M. Palanikumar, K. Arulmozhi","doi":"10.30538/psrp-odam2021.0056","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0056","url":null,"abstract":"We interact the theory of possibility Pythagorean bipolar fuzzy soft sets, possibility bipolar fuzzy soft sets and define complementation, union, intersection, AND and OR. The possibility Pythagorean bipolar fuzzy soft sets are presented as a generalization of soft sets. Notably, we tend to showed De Morgan’s laws, associate laws and distributive laws that are holds in possibility Pythagorean bipolar fuzzy soft set theory. Also, we advocate an algorithm to solve the decision making problem primarily based on soft set model.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129447431","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
Repeated sums and binomial coefficients 重复和和二项式系数
Open Journal of Discrete Applied Mathematics Pub Date : 2021-02-09 DOI: 10.30538/psrp-odam2021.0057
Roudy El Haddad
{"title":"Repeated sums and binomial coefficients","authors":"Roudy El Haddad","doi":"10.30538/psrp-odam2021.0057","DOIUrl":"https://doi.org/10.30538/psrp-odam2021.0057","url":null,"abstract":"Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial coefficient identities will be shown in order to prove this definition. Using this new definition, we simplify some particular sums such as the repeated Harmonic sum and the repeated Binomial-Harmonic sum. We derive formulae for simplifying general repeated sums as well as a variant containing binomial coefficients. Additionally, we study the (m)-th difference of a sequence and show how sequences whose (m)-th difference is constant can be related to binomial coefficients.","PeriodicalId":438929,"journal":{"name":"Open Journal of Discrete Applied Mathematics","volume":"50 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131810209","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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