Abstract: A graph G is
decomposable into the subgraphs of G
if no has isolated vertices and the edge
set can be partitioned into the subsets
If for every i,
we say that G is H-decomposable and we
write A graph F
without isolated vertices is a least common multiple of the graphs and if F
is a graph of minimum size such that F
is both
-decomposable and
-decomposable. The size (the number of edges) of a least common multiple of
two graphs and is denoted by Chartrand et al. [Periodica Math.
Hungar. 27(2) (1993),95-104] found and They also introduced a conjecture
about when n
is an odd integer Wang [Utilitas Math. 53 (1998),
231-242] proved the conjecture is true when We proved that the conjecture is
not true for some cases. For some cases we obtained a formula in [Far East J.
Appl. Math. 6(2) (2002), 191-200]. In this paper, we show that the conjecture is
true for the case when and is odd. When and where we establish a new formula.
Keywords and phrases: decomposition, least common multiple.
