Discussiones Mathematicae Graph Theory 31(2) (2011) 357-373
doi: 10.7151/dmgt.1551

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Petros A. Petrosyan

Institute for Informatics and Automation Problems
National Academy of Sciences, 0014, Armenia
Department of Informatics and Applied Mathematics
Yerevan State University, 0025, Armenia
e-mail: pet_petros@{ipia.sci.am, ysu.am, yahoo.com}


An edge coloring of a graph G with colors 1,2,…,t is called an interval t-coloring if for each i ∈ {1,2,…,t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let ℜ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if G,H ∈ ℜ, then the Cartesian product of these graphs belongs to ℜ. Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if G ∈ ℜ, then G[nK1] ∈ ℜ for any n ∈ ℕ. Furthermore, we show that if G,H ∈ ℜ and H is a regular graph, then strong and lexicographic products of graphs G,H belong to ℜ. We also prove that tensor and strong tensor products of graphs G,H belong to ℜ if G ∈ ℜ and H is a regular graph.

Keywords: edge coloring, interval coloring, regular graph, products of graphs.

2010 Mathematics Subject Classification: Primary: 05C15,
05C76; Secondary: 05C70.


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Received 20 November 2009
Revised 29 June 2010
Accepted 2 July 2010