Incidence coloring of Cartesian product graphs

Shiau, Alexander Chane; Shiau, Tzong-Huei; Wang, Yue-Li

doi:10.1016/j.ipl.2015.05.002

Cited by 5 publications

(1 citation statement)

References 9 publications

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“…Motivated by their research, we consider incidence coloring of Cartesian products of graphs; in particular we study sufficient conditions for the factors such that their Cartesian product is a (∆ + 2)-graph. Conjecture 2 has recently been confirmed also by Shiau, Shiau and Wang [13], who also considered Cartesian products of graphs, but in a different setting, not limiting to (∆ + 2)-graphs.…”

Section: Introductionmentioning

confidence: 68%

On incidence coloring conjecture in Cartesian products of graphs

Gregor

Lužar

Soták

2016

Discrete Applied Mathematics

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An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident to v. Two incidences (v, e) and (u, f ) are adjacent if at least one of the following holds: (a) v = u, (b) e = f , or (c) vu ∈ {e, f }. An incidence coloring of G is a coloring of its incidences assigning distinct colors to adjacent incidences. It was conjectured that at most ∆(G) + 2 colors are needed for an incidence coloring of any graph G. The conjecture is false in general, but the bound holds for many classes of graphs. We introduce some sufficient properties of the two factor graphs of a Cartesian product graph G for which G admits an incidence coloring with at most ∆(G) + 2 colors.

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Section: Introductionmentioning

confidence: 68%

On incidence coloring conjecture in Cartesian products of graphs

Gregor

Lužar

Soták

2016

Discrete Applied Mathematics

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Note on incidence chromatic number of subquartic graphs

2016

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Fuzzy incidence coloring on cartesian product of some fuzzy incidence graphs

Yamuna¹,

Prakash²

2023

IFS

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The Fuzzy Incidence Coloring (FIC) of a graph is a mapping of its Fuzzy Incidence set to a color set in which adjacent Fuzzy Incidences (FIs) are colored with different colors. Using various sorts of fuzzy graph products, new graphs can be created from two existing graphs. In this paper, we determined the Fuzzy Incidence Coloring Number (FICN) of some cartesian product with two Fuzzy Incidence Paths (FIPs) ( P m ˜ × P n ˜ ) , two Fuzzy Incidence cycles ( C m ˜ × C n ˜ ) , two Fuzzy Incidence complete graphs ( K m ˜ × K n ) ˜ , FIP, and Fuzzy Incidence cycle ( P m ˜ × C n ) ˜ , FIP and Fuzzy Incidence complete graph ( P m ˜ × K n ) ˜ , Fuzzy Incidence cycle and Fuzzy Incidence complete graph ( C m ˜ × K n ) ˜ , respectively.

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Incidence coloring of Cartesian product graphs

Cited by 5 publications

References 9 publications

On incidence coloring conjecture in Cartesian products of graphs

On incidence coloring conjecture in Cartesian products of graphs

Note on incidence chromatic number of subquartic graphs

Fuzzy incidence coloring on cartesian product of some fuzzy incidence graphs

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