Upper Bounds of Radio Number for Triangular Snake and Double Triangular Snake Graphs

Abstract

A radio labeling of a simple connected graph $G=\left(V,E\right)$ is a function $h:V⟶N$ such that $\left|h\left(x\right)-h\left(y\right)\right|\ge \text{diam}\left(G\right)+1-d\left(x,y\right)$ , where diam $\left(G\right)$ is the diameter of graph and d(x, y) is the distance between the two vertices. The radio number of $G$ , denoted by rn $\left(G\right)$ , is the minimum span of a radio labeling for $G$ . In this study, the upper bounds for radio number of the triangular snake and the double triangular snake graphs are introduced. The computational results indicate that the presented upper bounds are better than the results of the mathematical model provided by Badr and Moussa in 2020. On the contrary, these proposed upper bounds are better than the results of algorithms presented by Saha and Panigrahi in 2012 and 2018.