Even vertex anti-magic graceful labeling of graphs

Abstract

 An Even vertex anti-magic graceful labeling (EVAMGL) is a bijection function $f$:$V(G)\cup E(G)$ to $\{1, \ldots, p+q\}$ with the property that $f(E(G))=\{2, 4,\ldots ,2p\}$ and each $y\in V(G), \sum\limits_{z \in N(y)} f(yz) \\- f(y) = k$ consists of distinct integers. In this paper presents and examines a few fundamental characteristics of EVMGL. We demonstrate the existence of $E$-SVMGL for few families of graphs.