# Clique Decompositions of the Distance Multigraph of the Cartesian Product of Graphs

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Veerapas Boonthong

Chulalongkorn University

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**Minisymposium:**
GENERAL SESSION TALKS

**Content:**
The distance multigraph of a graph $G$ is the multigraph having the same vertex set as $G$ with $d_G(u, v)$ edges connecting each pair of vertices $u$ and $v$, where $d_G(u, v)$ is the distance between vertices $u$ and $v$ in a graph $G$. This work gives a technique to find a clique decomposition of the distance multigraph of the Cartesian product of graphs.