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T-Coloring of product graphs

Given a graph [Formula: see text] and a finite set [Formula: see text] of positive integers containing [Formula: see text] a [Formula: see text]-coloring of [Formula: see text] is a function [Formula: see text] for all [Formula: see text] in [Formula: see text] such that if [Formula: see text] then [Formula: see text] For a [Formula: see text]-coloring [Formula: see text] of [Formula: see text], the [Formula: see text]-span [Formula: see text] is the maximum value of [Formula: see text] over all pairs [Formula: see text] of vertices of [Formula: see text] The [Formula: see text]-span [Formula: see text] is the minimum [Formula: see text]-span overall [Formula: see text]-colorings of [Formula: see text]. The [Formula: see text]-edge span of a [Formula: see text]-coloring [Formula: see text] is the maximum value of [Formula: see text] over all edges [Formula: see text] of [Formula: see text]. The [Formula: see text]-edge span [Formula: see text] is the minimum [Formula: see text]-edge span overall [Formula: see text]-colorings of [Formula: see text]. This paper discusses the [Formula: see text]-span and [Formula: see text]-edge span of Cartesian, Join, Union and Tensor products of graphs. Also, we discuss the relation between Restricted span and Restricted edge span of graphs.

World Scientific Pub Co Pte Ltd

S. Jai Roselin

Discrete Mathematics, Algorithms and Applications

2021

Title: T-Coloring of product graphs

Description:

The [Formula: see text]-edge span of a [Formula: see text]-coloring [Formula: see text] is the maximum value of [Formula: see text] over all edges [Formula: see text] of [Formula: see text].

The [Formula: see text]-edge span [Formula: see text] is the minimum [Formula: see text]-edge span overall [Formula: see text]-colorings of [Formula: see text].

This paper discusses the [Formula: see text]-span and [Formula: see text]-edge span of Cartesian, Join, Union and Tensor products of graphs.

Also, we discuss the relation between Restricted span and Restricted edge span of graphs.

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