Chromaticity of some Tripartite Graphs - Yin, Jun; Zhao, Haixing; Ma, Xiujuan; Li, Yalan (Discontinuity, Nonlinearity, and Complexity, 2026)
For any graph $G$, we use $P(G, λ)$ to denote the the chromatic polynomial of $G$. Two graphs $G$ and $H$ are said to be equivalent, simply denoted by $G\sim H$, if $P(G, λ)=P(H, λ)$. Let $[G]=\{H|H\sim G\}$. $G$ is said to be chromatically unique if $[G]=\{G\}$. Let $K(n, n, n)$ be the complete tripartite graph with each part vertex set having $n$ vertice and $S$ be an edge set of $s$ edges in $K(n, n, n)$. In this paper, we give some chromatically unique tripartite graphs obtained by deleting some edges from $K(n, n, n)$ .