FORK-DECOMPOSITION OF TOTAL GRAPH OF CORONA GRAPHS

• Published in: TWMS journal of applied and engineering mathematics Vol. 14; no. 4; p. 1473
• Main Authors: Issacraj, A. Samuel, Joseph, J. Paulraj
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.09.2024; Elman Hasanoglu
• Subjects: Decomposition; Decomposition method; Graph theory; Graphs; Tests, problems and exercises; Vertex sets; India
• ISSN: 2146-1147; 2146-1147

Let G = (V, E) be a graph. Then the total graph of G is the graph T(G) with vertex set V(G) [union] E(G) in which two elements are adjacent if and only if they are either adjacent or incident with each other. The corona of two graphs [G.sub.1] and [G.sub.2], is the graph formed from one copy of [G.sub.1] and |V([G.sub.1])| copies of [G.sub.2] where the ith vertex of [G.sub.1] is adjacent to every vertex in the ith copy of [G.sub.2] and is denoted by [G.sub.1] [omicron] [G.sub.2]. Fork is a tree obtained by subdividing any edge of a star of size three exactly once. A decomposition of G is a partition of E(G) into edge disjoint subgraphs. If all the members of the partition are isomorphic to a subgraph H, then it is called a H-decomposition of G. In this paper, we investigate the existence of necessary and sufficient conditions for the fork-decomposition of Total graph of certain types of corona graphs which gives a partial solution for the conjecture of Barat and Thomassen [4] for graphs of small edge connectivity. Keywords: Graph decomposition, Total graph, Corona graph, Fork decomposition. AMS Subject Classification: 05C70, 05C51, 05C76.