Bounds of the Radio Number of Stacked-Book Graphs with Odd Paths

Abstract

A Stacked-book graph Gm,n is obtained from the Cartesian product of a star graph Sm and a path Pn, where m and s are the orders of the star graph and the path respectively. Obtaining the radio number of a graph is a rigorous process, which is dependent on the diameter of G and positive difference of non-negative integer labels f(u) and f(v) assigned to any two u, v in the vertex set V (G) of G. This paper obtains tight upper and lower bounds of the radio number of Gm,n where the path Pn has an odd order. The case where Pn has an even order has been investigated.