# Interval edge colorings of some products of graphs

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 2, page 357-373
- ISSN: 2083-5892

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topPetros A. Petrosyan. "Interval edge colorings of some products of graphs." Discussiones Mathematicae Graph Theory 31.2 (2011): 357-373. <http://eudml.org/doc/270969>.

@article{PetrosA2011,

abstract = {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 ∈ 𝔑, then the Cartesian product of these graphs belongs to 𝔑. Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if G ∈ 𝔑, then G[nK₁] ∈ 𝔑 for any n ∈ ℕ. Furthermore, we show that if G,H ∈ 𝔑 and H is a regular graph, then strong and lexicographic products of graphs G,H belong to 𝔑. We also prove that tensor and strong tensor products of graphs G,H belong to 𝔑 if G ∈ 𝔑 and H is a regular graph.},

author = {Petros A. Petrosyan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {edge coloring; interval coloring; regular graph; products of graphs},

language = {eng},

number = {2},

pages = {357-373},

title = {Interval edge colorings of some products of graphs},

url = {http://eudml.org/doc/270969},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Petros A. Petrosyan

TI - Interval edge colorings of some products of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 2

SP - 357

EP - 373

AB - 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 ∈ 𝔑, then the Cartesian product of these graphs belongs to 𝔑. Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if G ∈ 𝔑, then G[nK₁] ∈ 𝔑 for any n ∈ ℕ. Furthermore, we show that if G,H ∈ 𝔑 and H is a regular graph, then strong and lexicographic products of graphs G,H belong to 𝔑. We also prove that tensor and strong tensor products of graphs G,H belong to 𝔑 if G ∈ 𝔑 and H is a regular graph.

LA - eng

KW - edge coloring; interval coloring; regular graph; products of graphs

UR - http://eudml.org/doc/270969

ER -

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