Author

K. Somasundaram

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Preprint Sep 2026

Dominated Coloring of Some Classes of Perfect and Unicyclic Graphs

The dominated coloring of a graph $G$ is a proper vertex coloring such that each color class is dominated by a vertex. The minimum number of colors required for a dominated coloring of a graph $G$ is called the dominated chromatic number of the graph $G$ and is denoted by $\chi_{dom}(G)$. A graph $G$ is said to be chro...

R. Sneha, J. Geetha, K. Somasundaram · 0 citations

Preprint Sep 2026

Adjacent vertex distinguishing total chromatic number of graph products

The adjacent vertex distinguishing (AVD)-total chromatic number $\chi''_{a}(G)$ of a graph $G$ is the least integer $k$ for which $G$ has a proper total coloring $f$ with $k$ colors such that $C_G(u)\neq C_G(v)$ for every edge $uv\in E(G)$, where $C_G(u)=\{f(u)\}\cup\{f(uw):uw\in E(G)\}$. The AVD-total coloring conject...

A. Banerjee, J. Geetha, K. Somasundaram · 0 citations