Transactions on CombinatoricsTransactions on Combinatorics
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Feed provided by Transactions on Combinatorics. Click to visit.On numerical semigroups with embedding dimension three
http://toc.ui.ac.ir/article_20736_3875.html
Let $fneq1,3$ be a positive integer‎. ‎We prove that there exists a numerical semigroup $S$ with embedding dimension three such that $f$ is the Frobenius number of $S$‎. ‎We also show that‎ ‎the same fact holds for affine semigroups in higher dimensional monoids‎.Wed, 31 May 2017 19:30:00 +0100New class of integral bipartite graphs with large diameter
http://toc.ui.ac.ir/article_20738_0.html
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.Tue, 22 Nov 2016 20:30:00 +0100Full edge-friendly index sets of complete bipartite graphs
http://toc.ui.ac.ir/article_20739_3875.html
‎‎Let $G=(V,E)$ be a simple graph‎. ‎An edge labeling $f:Eto {0,1}$ induces a vertex labeling $f^+:VtoZ_2$ defined by $f^+(v)equiv sumlimits_{uvin E} f(uv)pmod{2}$ for each $v in V$‎, ‎where $Z_2={0,1}$ is the additive group of order 2‎. ‎For $iin{0,1}$‎, ‎let‎ ‎$e_f(i)=|f^{-1}(i)|$ and $v_f(i)=|(f^+)^{-1}(i)|$‎. ‎A labeling $f$ is called edge-friendly if‎ ‎$|e_f(1)-e_f(0)|le 1$‎. ‎$I_f(G)=v_f(1)-v_f(0)$ is called the edge-friendly index of $G$ under an edge-friendly labeling $f$‎. ‎The full edge-friendly index set of a graph $G$ is the set of all possible edge-friendly indices of $G$‎. ‎Full edge-friendly index sets of complete bipartite graphs will be determined‎.Wed, 31 May 2017 19:30:00 +0100Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs
http://toc.ui.ac.ir/article_20988_3875.html
‎Let $G$ be a graph and $chi^{prime}_{aa}(G)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎We prove a general bound for $chi^{prime}_{aa}(Gsquare H)$ for any two graphs $G$ and $H$‎. ‎We also determine‎ ‎exact value of this parameter for the Cartesian product of two paths‎, ‎Cartesian product of a path and a cycle‎, ‎Cartesian product of two trees‎, ‎hypercubes‎. ‎We show that $chi^{prime}_{aa}(C_msquare C_n)$ is at most $6$ fo every $mgeq 3$ and $ngeq 3$‎. ‎Moreover in some cases we find the exact value of $chi^{prime}_{aa}(C_msquare C_n)$‎.Wed, 31 May 2017 19:30:00 +0100A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs
http://toc.ui.ac.ir/article_21362_3875.html
Recently, E. M'{a}v{c}ajov'{a} and M. v{S}koviera proved that every bidirected Eulerian graph which admits a nowhere zero flow, admits a nowhere zero $4$-flow. This result shows the validity of Bouchet's nowhere zero conjecture for Eulerian bidirected graphs. In this paper we prove the same theorem in a different terminology and with a short and simple proof. More precisely, we prove that every Eulerian undirected graph which admits a zero-sum flow, admits a zero-sum $4$-flow. As a conclusion we obtain a shorter proof for the previously mentioned result of M'{a}v{c}ajov'{a} and v{S}koviera.Wed, 31 May 2017 19:30:00 +0100