Detour self-decomposition of corona product of graphs

Abstract

Decomposition of a graph G is the collection of edge-disjoint subgraphs of G. The longest distance between any two vertices of G is its detour distance. A subset S of V (G) is a detour set if every vertex of G lie on some u − v detour path, where u, v ∈ S. If a graph G can be decomposed into subgraphs G1,G2, ...,Gn with same detour number
as G then the decomposition Π = (G1,G2, ...,Gn) is called detour self-decomposition. The cardinality of maximum such possibility of detour self-decomposition in G is the detour self-decomposition number of G and is denoted by πsdn(G). The bounds of detour selfdecomposition number of corona product of graphs based on few properties have been discussed here.