4 – Roman Coloring Number for Some Classes of Standard Graphs

Chitra Ramaprakash¹ , Joseph Paul R.²

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.3 , pp.29-34, Jun-2023

Online published on Jun 30, 2023

Copyright © Chitra Ramaprakash, Joseph Paul R. . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A Roman coloring of a graph G is an assignment of four colors, {0, 1, 2, 3}, to the vertices of G such that every vertex with the color, 0 must be adjacent to some vertex of degree 2 or 3. And the color 1 can be adjacent to color 2 or color 3. In this paper, we extend the concept of Roman coloring to 4-coloring of graphs. We study the 4-Roman coloring of bull graphs and its related graphs for some standard class of graphs.

Key-Words / Index Term :
Roman Coloring, 4-Roman coloring, 4-Roman Chromatic Number, Triangular snakes, double triangular snakes, eccentricity, diameter, periphery

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