Transactions on CombinatoricsTransactions on Combinatorics
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http://iranjournals.nlai.ir/1481/
Feed provided by Transactions on Combinatorics. Click to visit.A Linear Algorithm for Computing $gamma_{_{[1,2]}}$-set in Generalized Series-Parallel Graphs
http://iranjournals.nlai.ir/1481/article_647211_86338.html
For a graph $G=(V,E)$, a set $S subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v in V setminus S$ is dominated by at most two vertices of $S$, i.e. $1 leq vert N(v) cap S vert leq 2$. Moreover a set $S subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 leq vert N(v) cap S vert leq 2$. The $[1,2]$-domination number of $G$, denoted $gamma_{[1,2]}(G)$, is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $gamma_{[1,2]}(G)$ is called a $gamma_{[1,2]}$-set. Total $[1,2]$-domination number and $gamma_{t[1,2]}$-sets of $G$ are defined in a similar way. This paper presents a linear time algorithm to find a $gamma_{[1,2]}$-set and a $gamma_{t[1,2]}$-set in generalized series-parallel graphs.Sat, 29 Feb 2020 20:30:00 +0100On a generalization of Leray simplicial complexes
http://iranjournals.nlai.ir/1481/article_647212_86338.html
We define a refinement of the notion of Leray simplicial complexes and study its properties. Moreover, we translate some of our results to the language of commutative algebra.Sat, 29 Feb 2020 20:30:00 +0100Bounds for metric dimension and defensive $k$-alliance of graphs under deleted lexicographic product
http://iranjournals.nlai.ir/1481/article_655301_86338.html
Metric dimension and defensive $k$-alliance number are two distance-based graph invariants which have applications in robot navigation, quantitative analysis of secondary RNA structures, national defense and fault-tolerant computing. In this paper, some bounds for metric dimension and defensive $k$-alliance of deleted lexicographic product of graphs are presented. We also show that the bounds are sharp.Sat, 29 Feb 2020 20:30:00 +0100Nilpotent graphs of skew polynomial rings over non-commutative rings
http://iranjournals.nlai.ir/1481/article_655302_86338.html
Let $R$ be a ring and $alpha$ be a ring endomorphism of $R$. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set $Z_N(R)^*$, and two distinct vertices $x$ and $y$ are connected by an edge if and only if $xy$ is nilpotent, where $Z_N(R)={xin R;|; xy; rm{is; nilpotent,;for; some}; yin R^*}.$ In this article, we investigate the interplay between the ring theoretical properties of a skew polynomial ring $R[x;alpha]$ and the graph-theoretical properties of its nilpotent graph $Gamma_N(R[x;alpha])$. It is shown that if $R$ is a symmetric and $alpha$-compatible with exactly two minimal primes, then $diam(Gamma_N(R[x,alpha]))=2$. Also we prove that $Gamma_N(R)$ is a complete graph if and only if $R$ is isomorphic to $Z_2timesZ_2$.Sat, 29 Feb 2020 20:30:00 +0100Transitive distance-regular graphs from linear groups $L(3,q)$, $q = 2,3,4,5$
http://iranjournals.nlai.ir/1481/article_655303_86338.html
In this paper we classify distance-regular graphs, including strongly regular graphs, admitting a transitive action of the linear groups $L(3,2)$, $L(3,3)$, $L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15. We give details about constructed graphs. In addition, we construct self-orthogonal codes from distance-regular graphs obtained in this paper.Sat, 29 Feb 2020 20:30:00 +0100