Analytic even mean labeling of some graphs

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 $f: V \rightarrow\{0,2,4,6, \ldots, 2 q\}$ with an induced edge labeling $f^*: E \rightarrow Z$ such that when each edge $e=u v$ with $f(u)<f(v)$ is labeled with $f^*(u v)=\left\lceil\frac{f(v)^2-(f(u)+1)^2}{2}\right\rceil$ if $f(u) \neq 0$ and $f^*(u v)=\left\lceil\frac{f(v)^2}{2}\right\rceil$ if $f(u)=0$, all the edge labels are even and distinct. We prove Jewel graph, Jelly Fish graph, Triangular Book graph, Triangular Book with Book Mark admits analytic even mean labeling.