Let L (K n) denote the line graph of the complete graph K n. Let α and β, β≠ 1, be non-
negative integers. Cox and Rodger (1996)[13] raised the following question: for what values …

By a {H 1 α, H 2 β, H 3 γ}-decomposition of a graph G, we mean a decomposition of G into α
copies of H 1, β copies of H 2 and γ copies of H 3, where α, β, γ are non-negative integers. In …

Let G be either a complete graph of odd order or a complete bipartite graph in which each
vertex partition has an even number of vertices. In this paper, we determine the set of triples …

Let H be a graph. A decomposition of H is a set of edge-disjoint subgraphs of H whose union
is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains …

The book Graph Theory and Decomposition covers major areas of the decomposition of
graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as …

This inaugural talk unveils the secrets of effective problem solving, delving into innovative
approaches that spark creativity. Drawing inspiration from the enchanting beauty of butterfly …

On Cyclic Near-Hamiltonian Cycle System of the Complete Multigraph Page 1 On Cyclic
Near-Hamiltonian Cycle System of the Complete Multigraph Raja'i Aldiabat1, a) and Haslinda …

Let  and  be positive integer,  denote a complete multigraph. A decomposition of a graph
 is a set of subgraphs of  whose edge sets partition the edge set of. The aim of this paper …

Graph theory is considered as a field exploring a large variety of proof techniques in discrete
mathematics. Thus, the various problems treated in this theory have applications in a lot of …

Let P_k denote a path on k vertices, and let S_k denote a star with k edges. For graphs F, G,
and H, a decomposition of F is a set of edge-disjoint subgraphs of F whose union is F. A (G …