On the $k$-distant total labeling of graphs
Authors :
Akul Rana
Author Address :
Department of Mathematics, Narajole Raj College, West Bengal-721211, India.
Abstract :
A labeling of a graph is a mapping that maps some set of graph elements to a set of numbers. In this paper, two new variations of labeling named $k$-distant edge total labeling and $k$-distant vertex total labeling are introduced. Moreover, the study of two new graph parameters, called $k$-distant edge chromatic number ($\gamma'_{kd}$) and $k$-distant vertex chromatic number ($\gamma_{kd}$) related this labeling are initiated. The $k$-distant vertex total labeling for paths, cycles, complete graphs, stars, bi-stars and friendship graphs are studied and the value of the parameter $\gamma_{kd}$ determined for these graph classes. Then $k$-distant edge total labeling for paths, cycles and stars are studied. Also, an upper bound of $\gamma_{kd}$ and a lower bound of $\gamma'_{kd}$ are presented for general graphs.
Keywords :
Graph Labeling, total labeling, $k$-distant vertex total labeling, $k$-distant edge total labeling.
DOI :
Article Info :
Received : January 09, 2020; Accepted : April 22, 2020.
