Least Common Multiple of Path, Star with Cartesian Product of Some Graphs 
Received:March 20, 2022 Revised:May 22, 2022 
Key Words:
graph decomposition least common multiple

Fund Project: 
Author Name  Affiliation  T. REJI  Department of Mathematics, Government College Chittur, Palakkad, Kerala, India  R. RUBY  Department of Mathematics, Government College Chittur, Palakkad, Kerala, India  B. SNEHA  Department of Mathematics, Government College Chittur, Palakkad, Kerala, India 

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Abstract: 
A graph $G$ without isolated vertices is a least common multiple of two graphs $H_1$ and $H_2$ if $G$ is a smallest graph, in terms of number of edges, such that there exists a decomposition of $G$ into edge disjoint copies of $H_1$ and $H_2$. The collection of all least common multiples of $ H_1 $ and $ H_2 $ is denoted by $ \LCM (H_1, H_2) $ and the size of a least common multiple of $ H_1 $ and $ H_2 $ is denoted by $ \lcm (H_1, H_2) $. In this paper $\lcm ( P_4, P_m\ \square\ P_n) $, $\lcm (P_4, C_m \ \square\ C_n)$ and $\lcm (K_{1,3}, K_{1,m}\ \square\ K_{1,n}) $ are determined. 
Citation: 
DOI:10.3770/j.issn:20952651.2023.01.002 
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