Transactions on CombinatoricsTransactions on Combinatorics
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Sun, 24 Feb 2019 03:18:18 +0100FeedCreatorTransactions on Combinatorics
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Feed provided by Transactions on Combinatorics. Click to visit.On the defensive alliances in graph
http://toc.ui.ac.ir/article_23227_4289.html
‎Let $ G = (V,E) $ be a graph‎. ‎We say that $ S subseteq V $ is a defensive alliance if for every $ u in S $‎, ‎the number of neighbors $ u $ has in $ S $ plus one (counting $ u $) is at least as large as the number of neighbors it has outside $ S $‎. ‎Then‎, ‎for every vertex $ u $ in a defensive alliance $ S $‎, ‎any attack on a single vertex by the neighbors of $ u $ in $ V-S $ can be thwarted by the neighbors of $ u $ in $ S $ and $ u $ itself‎. ‎In this paper‎, ‎we study alliances that are containing a given vertex $ u $ and study their mathematical properties‎.Thu, 28 Feb 2019 20:30:00 +0100On problems concerning fixed-point-free permutations and on the polycirculant conjecture-a survey
http://toc.ui.ac.ir/article_23166_4289.html
Fixed-point-free permutations‎, ‎also known as derangements‎, ‎have been studied for centuries‎. ‎In particular‎, ‎depending on their applications‎, ‎derangements of prime-power order and of prime order have always played a crucial role in a variety of different branches of mathematics‎: ‎from number theory to algebraic graph theory‎. ‎Substantial progress has been made on the study of derangements‎, ‎many long-standing open problems have been solved‎, ‎and many new research problems have arisen‎. ‎The results obtained and the methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs‎. ‎The methods used in this area range from deep group theory‎, ‎including the classification of the finite simple groups‎, ‎to combinatorial techniques‎. ‎This article is devoted to surveying results‎, ‎open problems and methods in this area‎.Thu, 28 Feb 2019 20:30:00 +0100On the double bondage number of graphs product
http://toc.ui.ac.ir/article_23167_0.html
A set $D$ of vertices of graph $G$ is called $double$ $dominating$ $set$ if for any vertex $v$, $|N[v]cap D|geq 2$. The minimum cardinality of $double$ $domination$ of $G$ is denoted by $gamma_d(G)$. The minimum number of edges $E'$ such that $gamma_d(Gsetminus E)>gamma_d(G)$ is called the double bondage number of $G$ and is denoted by $b_d(G)$. This paper determines that $b_d(Gvee H)$ and exact values of $b(P_ntimes P_2)$, and generalized corona product of graphs.Mon, 24 Dec 2018 20:30:00 +0100On the zero forcing number of generalized Sierpinski graphs
http://toc.ui.ac.ir/article_23265_4289.html
In this article we study the Zero forcing number of Generalized Sierpi'{n}ski graphs $S(G,t)$‎. ‎More precisely‎, ‎we obtain a general lower bound on the Zero forcing number of $S(G,t)$ and we show that this bound is tight‎. ‎In particular‎, ‎we consider the cases in which the base graph $G$ is a star‎, ‎path‎, ‎a cycle or a complete graph‎.Thu, 28 Feb 2019 20:30:00 +0100A lower bound on the k-conversion number of graphs of maximum degree k+1
http://toc.ui.ac.ir/article_23299_0.html
We derive a new sharp lower bound on the k-conversion number of graphs of maximum degree k+1. This generalizes a result of W. Staton [Induced forests in cubic graphs, Discrete Mathematics, 49(2):175--178, 1984], which established a lower bound on the k-conversion number of (k+1)-regular graphs.Sun, 03 Feb 2019 20:30:00 +0100VISUAL CRYPTOGRAPHY SCHEME ON GRAPHS
http://toc.ui.ac.ir/article_23300_0.html
Let $G=(V,E)$ be a connected graph and $Gamma (G)$ be the strong access structure where obtained from graph $G$. A visual cryptography scheme (VCS) for a set $P$ of participants is a method to encode a secret image such that any pixel of this image change to $m$ subpixels and only qualified sets can recover the secret image by stacking their shares. The value of $m$ is called the pixel expansion and the minimum value of the pixel expansion of a VCS for $Gamma (G)$ is denoted by $m^{*}(G)$. In this paper we obtain a characterization of all connected graphs $G$ with $m^{*}(G)=4$ and $omega (G)=5$ which $omega(G)$ is the clique number of graph $G$.Sun, 03 Feb 2019 20:30:00 +0100