Perfect 2-colorings of the line graphs of the connected bicubic graphs of order at most 12

Document Type : Research Articles

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Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

10.22080/cjms.2026.26918.1688

Abstract

Let $G =(V_G , E_G)$ be a graph and let $I$ be a finite set of size $m\geq 1$. A mapping $T:V_G \rightarrow I$ is called a perfect $m$-coloring with a parameter matrix $A = (a_{ij})_{i,j\in I }$ of $G$ if it is surjective and for all $i,j$, every vertex of color $i$ has $a_{i j}$ neighbors of color $j$. In this paper, we classify all the realizable parameter matrices of perfect 2-colorings of the line graphs of the connected bicubic graphs of order at most 12.

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