On conditional coloring of some graphs
P.Venkata Subba Reddy, K.Viswanathan Iyer

TL;DR
This paper investigates the conditional chromatic number of various graph classes, including grids, squares of cycles, strong products, and web graphs, providing specific values for different parameters.
Contribution
It determines the conditional chromatic number for several graph families under various conditions, extending existing coloring concepts.
Findings
Conditional chromatic number of grid graphs is established.
Results include the second order conditional chromatic number of (t,n)-web graphs.
Provides formulas for the conditional chromatic number of strong product graphs.
Abstract
For integers r and k > 0(k>r),a conditional (k, r)-coloring of a graph G is a proper k-coloring of G such that every vertex v of G has at least min{r,d(v)} differently colored neighbors, where d(v) is the degree of v. In this note, for different values of r we obtain the conditional chromatic number of a grid , and the strong product of and (n,m being positive integers). Also, for integers and the second order conditional chromatic number (also known as dynamic chromatic number) of the (t,n)-web graph is obtained.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Limits and Structures in Graph Theory
