ST-coloring of some products of graphs
Abstract
For a finite set T of non negative integers containing zero, a function c: V(G) → Z+∪{0} is said to be a ST-coloring of the graph G = (V,E), if |c(x) − c(y)| is not in T for any any edge (x, y) and for any two distinct edges (x, y) and (u, v), |c(x)−c(y)|≠|c(u)−c(v)|. spST (G) is the minimum of the difference between the largest and smallest colors assigned over all the vertices and espST (G) is the minimum of the maximum difference between the colors assigned to the vertices of an edge over all the edges of the graph, where the minimum is taken over all ST-coloring c. Here we establish some results related to ST-chromatic number, span and edge span of some graph products namely, Tensor product, Cartesian product and Corona product of graphs.
Copyright © 2020 Rubul Moran, Niranjan Bora, A. K. Baruah, A. Bharali. 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.
Cite this article
R. Moran, N. Bora, A. K. Baruah, A. Bharali, ST-coloring of some products of graphs, J. Math. Comput. Sci. 11 (2021), 337–347. https://doi.org/10.28919/jmcs/5099
BibTeX
@article{Moran2021,
author = {Moran, Rubul and Bora, Niranjan and Baruah, A. K. and Bharali, A.},
title = {ST-coloring of some products of graphs},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {337--347},
doi = {10.28919/jmcs/5099}
}