Abstract: A graph G is
said to be H-decomposable, denoted by if can be partitioned into subgraphs
such that each subgraph is isomorphic to h. Such a
factorization is called isomorphic factorization. If F is a graph of minimum size for which and then F
is called a least common multiple of and In this paper, we improve the
conjecture of Chartrand et al. [Periodica Mathematica Hungarica 27(2) (1993),
95‑104] and prove the conjecture is true in some cases. For some other
cases, we obtain new formulae.
Keywords and phrases: cycle, star, isomorphic factorization, least common multiple.
