Exceptionality of Edge Graceful Labeling of Tricycle Graphs

Abstract

Graceful labeling is assignment of distinct labels from $f\{0, |E|\}$ to vertices of graph, where edges are labeled by difference of absolute values of adjacent vertices and every label from $f\{1, 2, \dots, |E|\}$ is used exactly once as an edge label. The edge - gracefulness is reversal of gracefulness. It involves labeling edges, rather than vertices, with an induced numbering consisting of sums of edge- labels, rather than differences of vertex labels. In this paper, we are discussing about exceptionality of edge graceful labeling of tricycle graphs by the verification by Lo's theorem.