Ascending Chromatic Decomposition of Graphs

Nageswari A

Chromatic index | Decomposition

Vol: 8; Iss:11; Nov 22 | ISSN: 2454-5422

In this paper, we combine decomposition and domination and introduce the concept Ascending  Chromatic Decomposition (A‘D) of a graph G. An A‘D of a graph G is a collection ψ={G1,G2,…,Gn} of subgraphs of G such that, each Gi is connected, every edge of G is in exactly one Gi  and ‘Gi=i,1≤i≤n. Ascending Chromatic decomposition number of any graphG is the minimum number of decomposition in which A‘D exists and is denoted by AD‘(G). In this paper, we find Ascending chromatic decomposition number for Kn,Pn,Cn,Km,n .We also establish the necessary and sufficient condition for Ascending chromatic decomposition number exists in Km,n . We also find Ascending chromatic decomposition numbers for the corona of path cycle.