Some Results on Modified Mean Labeling of Graphs

Abstract

Let G be a graph with p vertices and q edges. Let $f : V (G)\to\{1,2,3,\dots,p\}$ be an bijective function. For a vertex labeling f, the induced edge labeling $f^{*}(e = uv)$ is defined by $f^{*}(e) = \frac{f\left(u\right)+f(v)}{2}$ if $f(u) + f(v)$ is even and $\frac{f\left(u\right)+f\left(v\right)-1}{2}$ if $f(u) + f(v)$ is odd, then f is called a modified \textit{mean} labeling if $\{f^{*}(e) / e \in E(G)\} = \{1,2,3,\dots,p-1\}$ and all are distinct integers. In the present work we investigate modified mean labeling of Paths, Caterpillar and Spider.