Recall that the minimum number of colors that allow a proper coloring of
graph $G$ is called the chromatic number of $G$ and denoted by $\chi(G).$ In
this paper the concepts of $\chi$'-chromatic sum and $\chi^+$-chromatic sum are
introduced. The extended graph $G^x$ of a graph $G$ was recently introduced for
certain regular graphs. We further the concepts of $\chi$'-chromatic sum and
$\chi^+$-chromatic sum to extended paths and cycles. The paper concludes with
\emph{patterned structured} graphs.Comment: 12 page

Bej, Saptarshi

Kok, Johan

Journal of Algebra Combinatorics Discrete Structures and Applications

English

arXiv

We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\chi(G)$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\chi'$-chromatic sum and $\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\chi'$-chromatic sum and $\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures

Coloring Sums of Extensions of Certain Graphs

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Journal of Algebra Combinatorics Discrete Structures and Applications (JACODESMATH, Yildiz Technical University - YTU)

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