Edge even graceful labelling of some book 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 if there is a bijection f from the edges of the graph to the set {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. They proved necessary and sufficient conditions for some path and cycle-related graphs to be edge even graceful. In this paper we proved that triangular book graphs and quadrilateral book graphs admit edge even graceful labelling.

Network Coherence in a Family of Book Graphs

“…In this paper, a family of book graphs is chosen as our network models. The topological indices, e.g., randic index, sum connectivity index, geometricarithmetic index, fourth atom-bond connectivity index, and edge labeling, have been analytically obtained [24,25]. However, the dynamics of the book graphs remains less understood, in spite of the facts that studying the dynamical processes leads to a better understanding of how the underlying systems work.…”

Edge even graceful labelling of new families of graphs

“…In 2018, authors [14], proved that triangular book graphs and quadrilateral book graphs admit edge even graceful labelling. In this paper we proved that double fan graphs and quadrilateral friendship admit edge even graceful labelling.…”