Edge even graceful labelling of new families of graphs

Abstract

Elsonbaty and Daoud introduced a new type of labelling of a graph G with p vertices and q edges called an edge even graceful labelling. A graph G is called edge even graceful if there is a bijection f : E(G) → {2, 4,. .. , 2q} such that, when each vertex is assigned the sum of all edges incident to it mod 2k, where k = max(p, q), the resulting vertex labels are distinct. In this paper we proved that double fan graphs, quadrilateral friendship graphs, and butterfly graphs are edge even graceful graphs.

On total edge irregularity strength of polar grid graph

“…On the other hand, in [6][7][8] the total edge irregularity strengths for fan graph, wheel graph, triangular Book graph, friendship graph, centralized uniform theta graphs and large graphs are investigated. For definitions, applications and terminology are not mentioned in our paper, see [5,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”