Transactions on CombinatoricsTransactions on Combinatorics
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Fri, 19 Apr 2019 01:53:25 +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 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 +0100On the double bondage number of graphs products
http://toc.ui.ac.ir/article_23167_4289.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.Thu, 28 Feb 2019 20:30:00 +0100Visual cryptography scheme on graphs with \boldmath $m^{*}(G)=4$
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 +0100A note on some lower bounds of the Laplacian energy of a graph
http://toc.ui.ac.ir/article_23370_0.html
‎For a simple connected graph $G$ of order $n$ and size $m$‎, ‎the Laplacian energy of $G$ is defined as‎ ‎$LE(G)=sum_{i=1}^n|mu_i-frac{2m}{n}|$ where $mu_1‎, ‎mu_2,ldots‎,‎‎mu_{n-1}‎, ‎mu_{n}$‎ ‎are the Laplacian eigenvalues of $G$ satisfying $mu_1ge mu_2gecdots ge mu_{n-1}>‎ ‎mu_{n}=0$‎. ‎In this note‎, ‎some new lower bounds on the graph invariant $LE(G)$ are derived‎. ‎The obtained results are compared with some already known lower bounds of $LE(G)$‎.Fri, 01 Mar 2019 20:30:00 +0100Bounds for the skew Laplacian (skew adjacency) spectral radius of a digraph
http://toc.ui.ac.ir/article_23413_0.html
‎For a simple connected graph $G$ with $n$ vertices and $m$ edges‎, ‎let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$‎. ‎In this paper‎, ‎we consider the skew Laplacian/skew adjacency matrix of the digraph $overrightarrow{G}$‎. ‎We obtain upper bounds for the skew Laplacian/skew adjacency spectral radius‎, ‎in terms of various parameters (like oriented degree‎, ‎average oriented degree) associated with the structure of the digraph $overrightarrow{G}$‎. ‎We also obtain upper and lower bounds for the skew Laplacian/skew adjacency spectral radius‎, ‎in terms of skew Laplacian/skew adjacency rank of the digraph $overrightarrow{G}$‎.Tue, 05 Mar 2019 20:30:00 +0100A note on fall colorings of Kneser graphs
http://toc.ui.ac.ir/article_23510_0.html
A fall coloring of a graph $G$ is a proper coloring of $G$ with $k$ colors such that each vertex sees all $k$colors on its closed neighborhood. In this short note, we characterizeall fall colorings of Kneser graphs of type $KG(n,2)$.Tue, 26 Mar 2019 19:30:00 +0100A note on full weight spectrum codes
http://toc.ui.ac.ir/article_23512_0.html
A linear $ [n,k]_q $ code $ C $ is said to be a full weight spectrum (FWS) code if there exist codewords of each weight less than or equal to $ n $. In this brief communication we determine necessary and sufficient conditions for the existence of linear $ [n,k]_q $ full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in $ PG(k-1,q) $.Fri, 29 Mar 2019 19:30:00 +0100