2019-05-21T18:13:06Z http://toc.ui.ac.ir/?_action=export&rf=summon&issue=4083
2018-03-01 10.22108
Transactions on Combinatorics Trans. Comb. 2251-8657 2251-8657 2018 7 1 Annihilating submodule graph for modules Saeed Safaeeyan Let \$R\$ be a commutative ring and \$M\$ an‎ ‎\$R\$-module‎. ‎In this article‎, ‎we introduce a new generalization of‎ ‎the annihilating-ideal graph of commutative rings to modules‎. ‎The‎ ‎annihilating submodule graph of \$M\$‎, ‎denoted by \$Bbb G(M)\$‎, ‎is an‎ ‎undirected graph with vertex set \$Bbb A^*(M)\$ and two distinct‎ ‎elements \$N\$ and \$K\$ of \$Bbb A^*(M)\$ are adjacent if \$N*K=0\$‎. ‎In‎ ‎this paper we show that \$Bbb G(M)\$ is a connected graph‎, ‎\${rm‎ ‎diam}(Bbb G(M))leq 3\$‎, ‎and \${rm gr}(Bbb G(M))leq 4\$ if \$Bbb‎ ‎G(M)\$ contains a cycle‎. ‎Moreover‎, ‎\$Bbb G(M)\$ is an empty graph‎ ‎if and only if \${rm ann}(M)\$ is a prime ideal of \$R\$ and \$Bbb‎ ‎A^*(M)neq Bbb S(M)setminus {0}\$ if and only if \$M\$ is a‎ ‎uniform \$R\$-module‎, ‎\${rm ann}(M)\$ is a semi-prime ideal of \$R\$‎ ‎and \$Bbb A^*(M)neq Bbb S(M)setminus {0}\$‎. ‎Furthermore‎, ‎\$R\$‎ ‎is a field if and only if \$Bbb G(M)\$ is a complete graph‎, ‎for‎ ‎every \$Min R-{rm Mod}\$‎. ‎If \$R\$ is a domain‎, ‎for every divisible‎ ‎module \$Min R-{rm Mod}\$‎, ‎\$Bbb G(M)\$ is a complete graph with‎ ‎\$Bbb A^*(M)=Bbb S(M)setminus {0}\$‎. ‎Among other things‎, ‎the‎ ‎properties of a reduced \$R\$-module \$M\$ are investigated when‎ ‎\$Bbb G(M)\$ is a bipartite graph‎. ‎Module‎ ‎Annihilating submodule graph‎ ‎Complete graph 2018 03 01 1 12 http://toc.ui.ac.ir/article_21462_0dc774d0c7d8fb2042f09cc2cf66d2ad.pdf
2018-03-01 10.22108
Transactions on Combinatorics Trans. Comb. 2251-8657 2251-8657 2018 7 1 New class of integral bipartite graphs with large diameter Alireza Fiuj Laali Hamid Haj Seyyed Javadi In this paper‎, ‎we construct a new class of integral bipartite graphs (not necessarily trees) with large even diameters‎. ‎In fact‎, ‎for every finite set \$A\$ of positive integers of size \$k\$ we construct an integral bipartite graph \$G\$ of diameter \$2k\$ such that the set of positive eigenvalues of \$G\$ is exactly \$A\$‎. ‎This class of integral bipartite graphs has never found before‎. Integral graph Diameter root 2018 03 01 13 17 http://toc.ui.ac.ir/article_20738_4ef9fcdc49725050979fd7bbc4a6836d.pdf
2018-03-01 10.22108
Transactions on Combinatorics Trans. Comb. 2251-8657 2251-8657 2018 7 1 Majorization and the number of bipartite graphs for given vertex degrees Annabell Berger The emph{bipartite realisation problem} asks for a pair of non-negative‎, ‎non-increasing integer lists \$a:=(a_1,ldots,a_n)\$ and \$b:=(b_1,ldots,b_{n'})\$ if there is a labeled bipartite graph \$G(U,V,E)\$ (no loops or multiple edges) such that each vertex \$u_i in U\$ has degree \$a_i\$ and each vertex \$v_i in V\$ degree \$b_i.\$ The Gale-Ryser theorem provides characterisations for the existence of a `realisation' \$G(U,V,E)\$ that are strongly related to the concept of emph{majorisation}‎. ‎We prove a generalisation; list pair \$(a,b)\$ has more realisations than \$(a',b),\$ if \$a'\$ majorises \$a.\$ Furthermore‎, ‎we give explicitly list pairs which possess the largest number of realisations under all \$(a,b)\$ with fixed \$n\$‎, ‎\$n'\$ and \$m:=sum_{i=1}^n a_i.\$ We introduce the notion~emph{minconvex list pairs} for them‎. ‎If \$n\$ and \$n'\$ divide \$m,\$ minconvex list pairs turn in the special case of two constant lists \$a=(frac{m}{n},ldots,frac{m}{n})\$ and \$b=(frac{m}{n'},ldots,frac{m}{n'}).\$‎ bigraphic sequence‎ ‎matrices with fixed row and column sums‎ ‎contingency tables with fixed margins‎ ‎bipartite realisation problem‎ ‎Gale-Ryser theorem 2018 03 01 19 30 http://toc.ui.ac.ir/article_21469_4550ee854fabeca9498c8036d49fbd87.pdf
2018-03-01 10.22108
Transactions on Combinatorics Trans. Comb. 2251-8657 2251-8657 2018 7 1 Products of graphs and Nordhaus-Gaddum type inequalities for eigenvalues Nastaran Keyvan Farhad Rahmati In this paper‎, ‎we obtain \$alpha\$ as coefficient for the \$G=K_{alpha n} cup overline{K_{(1-alpha)n}}\$ and by which we discuss Nikiforov's conjecture for \$lambda_{1}\$ and Aouchiche and Hansen's conjecture for \$q_1\$ in Nordhaus-Gaddum type inequalities‎. ‎Furthermore‎, ‎by the properties of the products of graphs we put forward a new approach to find some bounds of Nordhaus-Gaddum type inequalities‎. Nordhaus-Gaddum inequalities extremal graphs product of graphs 2018 03 01 31 36 http://toc.ui.ac.ir/article_21474_4d4d47f1c8519b0e97e542738798fb06.pdf
2018-03-01 10.22108
Transactions on Combinatorics Trans. Comb. 2251-8657 2251-8657 2018 7 1 PD-sets for codes related to flag-transitive symmetric designs Dean Crnkovic Nina Mostarac ‎For any prime \$p\$ let \$C_p(G)\$ be the \$p\$-ary code spanned by the rows of the incidence matrix \$G\$ of a graph \$Gamma\$‎. ‎Let \$Gamma\$ be the incidence graph of a flag-transitive symmetric design \$D\$‎. ‎We show that any flag-transitive‎ ‎automorphism group of \$D\$ can be used as a PD-set for full error correction for the linear code \$C_p(G)\$‎ ‎(with any information set)‎. ‎It follows that such codes derived from flag-transitive symmetric designs can be‎ ‎decoded using permutation decoding‎. ‎In that way to each flag-transitive symmetric \$(v‎, ‎k‎, ‎lambda)\$ design we associate a linear code of length \$vk\$ that is‎ ‎permutation decodable‎. ‎PD-sets obtained in the described way are usually of large cardinality‎. ‎By studying codes arising from some flag-transitive symmetric designs we show that smaller PD-sets can be found for‎ ‎specific information sets‎. Code graph flag-transitive design permutation decoding 2018 03 01 37 50 http://toc.ui.ac.ir/article_21615_538caf5ff8ba2437eee5ab750d6dce2a.pdf