Let G = {V(G), E(G)} be a simple connected graph with diameter d(G) and k be a positive integer. A radio k-coloring of a graph is a proper node coloring that is an assignment f of positive integers to the nodes of G such that  where x and y are two distinct nodes, and d(x, y) is the length between x and y.  The maximum color assigned to some node of f(V(G)) is called the span of f and it is indicated by span(f). The least span over all radio k-coloring of G is the radio k-chromatic number of G and it is indicated by rc_k(G). In this paper, we investigate the radio k-chromatic number for the triple star graph K_{1, n,n,n} and its middle graph M(K_{1, n, n, n}), central graph M(K_{1, n, n, n}), total graph  T(K_{1, n, n, n}) and line graph L(K_{1, n, n, n}).

radio k-coloring, radio k-chromatic number, triple star graph, middle graph, central graph, total graph, line graph.

Received: October 4, 2023; Revised: November 22, 2023; Accepted: February 6, 2024; Published: September 28, 2024

How to cite this article: P. Kowsalya and D. Vijayalakshmi, On radio k-chromatic numbers  for the family of triple star graphs, Far East Journal of Applied Mathematics 117(2) (2024), 169-181. http://dx.doi.org/10.17654/0972096024009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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