## SOME RESULTS ON ANALYTIC EVEN MEAN LABELING OF GRAPH

## T. S. Kumari, M. Regees and S. C. Kumar

** DOI:**

https://doi.org/10.37418/amsj.9.4.71

Abstract

Let $G(V,E)$ be a graph with $p$ vertices and $q$ edges. $A(p,q)$- graph $G$ is called an analytic even mean graph if there exist an injective function $f:V\rightarrow \{0, 2, 4, 6,…, 2q\}$ with an induced edge labeling $f^{*}:E\rightarrow Z$ such that when each edge $e=uv$ with $f(u)<f(v)$ is labeled with $f^{*}(uv)=\left\lceil \frac{f(v)^{2}-(f(u)+1)^2}{2}\right\rceil$ if $f(u)\neq 0$ and $f^{*}(uv)=\left\lceil \frac{f(v)^2}{2}\right\rceil$ if $f(u)=0$, all the edge labels are even and distinct. In this paper we show the analytic even mean labeling of coconut tree graph, fire cracker graph and some other results.

**Keywords: **Mean labeling, Analytic mean labeling, Analytic even mean labeling, Coconut tree graph, Fire cracker graph.