Transactions on CombinatoricsTransactions on Combinatorics
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Feed provided by Transactions on Combinatorics. Click to visit.Coloring problem of signed interval graphs
http://toc.ui.ac.ir/article_23849_4289.html
A signed graph $(G,sigma)$ is a graph‎ ‎together with an assignment of signs ${+,-}$ to its edges where‎ ‎$sigma$ is the subset of its negative edges‎. ‎There are a few variants of coloring and clique problems of‎ ‎signed graphs‎, ‎which have been studied‎. ‎An initial version known as vertex coloring of signed graphs is defined by Zaslavsky in $1982$‎. ‎Recently Naserasr et. al., in [R‎. ‎Naserasr‎, ‎E‎. ‎Rollova and E‎. ‎Sopena‎, ‎Homomorphisms of signed graphs‎, ‎J‎. ‎Graph Theory‎, 79‎‎ (2015) 178--212, have defined signed chromatic and signed clique numbers of signed graphs‎. ‎In this paper we consider the latter mentioned problems for signed interval graphs‎. ‎We prove that the coloring problem of signed‎ ‎interval graphs is NP-complete whereas their ordinary coloring‎ ‎problem (the coloring problem of interval graphs) is in P‎. ‎Moreover we prove that the signed clique problem of a‎ ‎signed interval graph can be solved in polynomial time‎. ‎We also consider the‎ ‎complexity of further related problems‎. Sat, 30 Nov 2019 20:30:00 +0100Elliptic root systems of type $A_1$, a combinatorial study
http://toc.ui.ac.ir/article_24023_0.html
We consider some combinatorics of elliptic root systems of type $A_1$. In particular, with respect to a fixed reflectable base, we give a precise description of the positive roots in terms of a ``positivity'' theorem. Also the set of reduced words of the corresponding Weyl group is precisely described. These then lead to a new characterization of the core of the corresponding Lie algebra, namely we show that the core is generated by positive root spaces.Thu, 10 Oct 2019 20:30:00 +0100GENERALIZED ZAGREB INDEX OF PRODUCT GRAPHS
http://toc.ui.ac.ir/article_24024_0.html
The generalized Zagreb index is an extension of both ordinary and variable Zagreb indices.In this paper, we present exact formulae for the values of the generalized Zagreb index for product graphs. Results are applied to some graphs of general and chemical interest such as nanotubes and nanotori.Thu, 10 Oct 2019 20:30:00 +0100