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Bipolar Fuzzy Competition Graphs 双极模糊竞争图
Ars Comb. Pub Date : 2020-11-03 DOI: 10.1007/978-981-15-8756-6_4
N. Alshehri, M. Akram
{"title":"Bipolar Fuzzy Competition Graphs","authors":"N. Alshehri, M. Akram","doi":"10.1007/978-981-15-8756-6_4","DOIUrl":"https://doi.org/10.1007/978-981-15-8756-6_4","url":null,"abstract":"","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121993633","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: 34
On super edge magic deficiency of kite graphs 论风筝图的超边魔法缺陷
Ars Comb. Pub Date : 2020-01-11 DOI: 10.12732/ijam.v32i6.6
A. Ahmad, M. K. Siddiqui, M. Nadeem, M. Imran
{"title":"On super edge magic deficiency of kite graphs","authors":"A. Ahmad, M. K. Siddiqui, M. Nadeem, M. Imran","doi":"10.12732/ijam.v32i6.6","DOIUrl":"https://doi.org/10.12732/ijam.v32i6.6","url":null,"abstract":"Abstract: An edge magic labeling of a graph G is a bijection λ : V (G) ∪ E(G) → {1, 2, . . . , |V (G)|+|E(G)|} such that λ(u)+λ(uv)+λ(v) is constant, for every edge uv ∈ E(G). The concept of edge magic deficiency was introduce by Kotzig and Rosas. Motivated by this concept Figueroa-Centeno, Ichishima and Muntaner-Batle defined a similar concept for super edge magic total labelings. The super edge magic deficiency of a graph G, which is denoted by μs(G), is the minimum nonnegative integer n such that G∪nK1, has a super edge magic total labeling or it is equal to +∞ if there exists no such n. In this paper, we study the super edge magic deficiency of kite graphs.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122264259","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: 6
Sufficient conditions for maximally edge-connected and super-edge-connected oriented graphs depending on the clique number 基于团数的最大边连通和超边连通定向图的充分条件
Ars Comb. Pub Date : 2017-06-01 DOI: 10.22049/CCO.2017.13594
L. Volkmann
{"title":"Sufficient conditions for maximally edge-connected and super-edge-connected oriented graphs depending on the clique number","authors":"L. Volkmann","doi":"10.22049/CCO.2017.13594","DOIUrl":"https://doi.org/10.22049/CCO.2017.13594","url":null,"abstract":"Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximallyedge-connected or super-edge-connected if the numberof edges is large enough. Examples will demonstrate that our conditions are sharp.noindent {bf Keywords:} Edge-connectivity; Maximally edge-connected graphs; Super-edge-connectedgraphs","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125761462","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
Twin signed total domination numbers in directed graphs 有向图中的双签名总支配数
Ars Comb. Pub Date : 2016-09-30 DOI: 10.5556/J.TKJM.47.2016.2035
M. Atapour, A. Bodaghli, S. M. Sheikholeslami
{"title":"Twin signed total domination numbers in directed graphs","authors":"M. Atapour, A. Bodaghli, S. M. Sheikholeslami","doi":"10.5556/J.TKJM.47.2016.2035","DOIUrl":"https://doi.org/10.5556/J.TKJM.47.2016.2035","url":null,"abstract":"Let $D$ be a finite simple digraph with vertex set $V(D)$ and arc set $A(D)$. A twin signed Roman dominating function (TSRDF) on the digraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfying the conditions that (i) $sum_{xin N^-[v]}f(x)ge 1$ and $sum_{xin N^+[v]}f(x)ge 1$ for each $vin V(D)$, where $N^-[v]$ (resp. $N^+[v]$) consists of $v$ and all in-neighbors (resp. out-neighbors) of $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an in-neighbor $v$ and an out-neighbor $w$ for which $f(v)=f(w)=2$. The weight of an TSRDF $f$ is $omega(f)=sum_{vin V(D)}f(v)$. The twin signed Roman domination number $gamma_{sR}^*(D)$ of $D$ is the minimum weight of an TSRDF on $D$. In this paper, we initiate the study of twin signed Roman domination in digraphs and we present some sharp bounds on $gamma_{sR}^*(D)$. In addition, we determine the twin signed Roman domination number of some classes of digraphs.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129833429","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
Computing Wiener Index of C12n Fullerenes 计算C12n富勒烯的Wiener指数
Ars Comb. Pub Date : 2015-08-01 DOI: 10.1166/JCTN.2015.3968
M. Ghorbani, M. Songhori
{"title":"Computing Wiener Index of C12n Fullerenes","authors":"M. Ghorbani, M. Songhori","doi":"10.1166/JCTN.2015.3968","DOIUrl":"https://doi.org/10.1166/JCTN.2015.3968","url":null,"abstract":"","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124711169","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
Number of Spanning trees in Different Products of Complete and Complete Tripartite Graphs 完备三部图与完备三部图不同积中的生成树数目
Ars Comb. Pub Date : 2014-07-02 DOI: 10.1155/2014/965105
S. N. Daoud
{"title":"Number of Spanning trees in Different Products of Complete and Complete Tripartite Graphs","authors":"S. N. Daoud","doi":"10.1155/2014/965105","DOIUrl":"https://doi.org/10.1155/2014/965105","url":null,"abstract":"Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115384294","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: 11
The Maximal Total Irregularity of Unicyclic Graphs 单环图的最大全不规则性
Ars Comb. Pub Date : 2014-04-10 DOI: 10.1155/2014/785084
L. You, Jieshan Yang, Zhifu You
{"title":"The Maximal Total Irregularity of Unicyclic Graphs","authors":"L. You, Jieshan Yang, Zhifu You","doi":"10.1155/2014/785084","DOIUrl":"https://doi.org/10.1155/2014/785084","url":null,"abstract":"In 2012, Abdo and Dimitrov defined the total irregularity of a graph as , where denotes the vertex degree of a vertex . In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs on vertices.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123491231","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
Conditional Matching Preclusion For The Star Graphs 星图的条件匹配排除
Ars Comb. Pub Date : 2013-03-27 DOI: 10.1142/S0129626413500047
E. Cheng, László Lipták, Lih-Hsing Hsu, Jimmy J. M. Tan, Cheng-Kuan Lin
{"title":"Conditional Matching Preclusion For The Star Graphs","authors":"E. Cheng, László Lipták, Lih-Hsing Hsu, Jimmy J. M. Tan, Cheng-Kuan Lin","doi":"10.1142/S0129626413500047","DOIUrl":"https://doi.org/10.1142/S0129626413500047","url":null,"abstract":"The matching preclusion number of an even graph G, denoted by mp(G), is the minimum number of edges whose deletion leaves the resulting graph without perfect matchings. The conditional matching preclusion number of an even graph G, denoted by mp1(G), is the minimum number of edges whose deletion leaves the resulting graph with neither perfect matchings nor isolated vertices. The class of (n,k)-star graphs is a popular class of interconnection networks for which the matching preclusion number and the classification of the corresponding optimal solutions were known. However, the conditional version of this problem was open. In this paper, we determine the conditional matching preclusion for (n,k)-star graphs as well as classify the corresponding optimal solutions via several new results. In addition, an alternate proof of the results on the matching preclusion problem will also be given.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126879410","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: 12
On the endomorphism monoid of K(n, 4) 关于K(n, 4)的自同态单群
Ars Comb. Pub Date : 2012-07-05 DOI: 10.1142/S1005386712000302
Hailong Hou, Rui Gu
{"title":"On the endomorphism monoid of K(n, 4)","authors":"Hailong Hou, Rui Gu","doi":"10.1142/S1005386712000302","DOIUrl":"https://doi.org/10.1142/S1005386712000302","url":null,"abstract":"In this paper, the endomorphism monoid of circulant complete graph K(n,3) is explored explicitly. It is shown that AutK(n,3)) =Dn, the dihedral group of degree n. It is also shown that K(n,3) is unretractive when 3 does not divide n, End(K(3m,3)) =qEnd(K(3m,3)), sEnd(K(3m,3)) =Aut(K(3m,3)) and K(3m,3) is endomorphism-regular. The structure of End(K(3m,3)) is characterized and some enumerative problems concerning End(K(n,3)) are solved.","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132125625","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
On Harmonious Labelings of the Balanced Quadruple Shells 论平衡四重壳的和谐标记
Ars Comb. Pub Date : 2011-09-17 DOI: 10.1007/978-3-642-24097-3_32
Yuansheng Yang, Xirong Xu, Xi Yue, Qiao Jing
{"title":"On Harmonious Labelings of the Balanced Quadruple Shells","authors":"Yuansheng Yang, Xirong Xu, Xi Yue, Qiao Jing","doi":"10.1007/978-3-642-24097-3_32","DOIUrl":"https://doi.org/10.1007/978-3-642-24097-3_32","url":null,"abstract":"","PeriodicalId":378960,"journal":{"name":"Ars Comb.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132310983","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
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