Maximum Degree Based Vertex Graceful Labeling Graph with Even Labeling on Edges

Abstract

We characterized and illustrated the concept of maximum degree based vertex graceful labeling graph with even labeling on edges in this paper. It is a particular type of labeling vertex of a graph G with p vertices and q edges if there exists a bijection f from the edge set to the set $\left\{ {2, 4, 6, \ldots ,2q} \right\}$ so that the induced mapping $f^{*} :V \to \left\{ {0, 1, 2, \ldots , \left( {2q - 1} \right)} \right\}$ which is given by $f^{*} \left( u \right) = \left\{ {{{\left[ {\frac{{\sum f\left( {uv} \right)}}{\Delta }} \right]} \mathord{\left/ {\vphantom {{\left[ {\frac{{\sum f\left( {uv} \right)}}{\Delta }} \right]} {uv}}} \right. \kern-0pt} {uv}} \in E\left( G \right)} \right\}$, where $\Delta$ is maximum degree of G, [ ] denotes the integral part. In this, we proved path, cycle, and crown graph as maximum degree-based vertex graceful labeling graph with even labeling on edges.