# Common Multiples of Paths and Stars with Crowns

## Authors

• Saritha Chandran C. Government Victoria College.
• Reji T. Government College Chittur.

## Keywords:

Graph Decomposition, Common Multiples of Graphs, Path, Star, Crown

## Abstract

{\footnotesize A graph \$G\$ is a common multiple of two graphs \$H_1\$ and \$H_2\$ if there exists a decomposition of \$G\$ into edge-disjoint copies of \$H_1\$ and also a decomposition of \$G\$ into edge-disjoint copies of \$H_2\$. If \$ G \$ is a common multiple of \$H_1\$ and \$H_2\$, and \$ G \$ has \$ q \$ edges, then we call \$ G \$ a \$ (q, H_1, H_2) \$ graph. Our paper deals with the following question: Given two graphs \$ H_1 \$ and \$ H_2\$, for which values of \$ q \$ does there exist a \$ (q, H_1, H_2) \$ graph? when \$H_1\$ is either a path or a star with \$3\$ or \$4\$ edges and \$H_2\$ is a crown.
}

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2024-04-03

Artículos

## How to Cite

[1]
“Common Multiples of Paths and Stars with Crowns ”, Proyecciones (Antofagasta, On line), vol. 43, no. 2, pp. 331–344, Apr. 2024, doi: 10.22199/issn.0717-6279-5720.