The edge geodetic self decomposition number of a graph

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 p of edge-disjoint subgraphs G1;G2; : : : ;Gn of G such that every edge of G belongs to exactly one Gi(1 ≤i ≤ n). The decomposition = fG1;G2; : : : ;Gng of a connected graph G is said to be an edge geodetic self decomposition, if ge(Gi) = ge(G) for all i(1 ≤ i ≤ n). The maximum cardinality of is called the edge geodetic self decomposition number of G and is denoted by πsge (G), where ge(G) is the edge geodetic number of G. Some general properties satisffed by this concept are studied.