The edge geodetic self decomposition number of a graph

¹ Department of Mathematics, Government College of Engineering, Tirunelveli 627007, India
² Department of Mathematics, St. Alphonsa College of Arts and Science, Soosaipuram, Karungal 629157, India

^* Corresponding author: john@gcetly.ac.in

Received: 13 October 2019
Accepted: 26 June 2020

Abstract

Let G = (V, E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection π of edge-disjoint subgraphs G₁, G₂, … , G_n of G such that every edge of G belongs to exactly one G_i(1 ≤ i ≤ n). The decomposition π = {G₁, G₂, … , G_n} of a connected graph G is said to be an edge geodetic self decomposition, if g_e(G_i) = g_e(G) for all i(1 ≤ i ≤ n). The maximum cardinality of π is called the edge geodetic self decomposition number of G and is denoted by π_sge(G), where g_e(G) is the edge geodetic number of G. Some general properties satisfied by this concept are studied.