IRREGULAR COLORING OF SOME SPECIAL GRAPHS

R. Avudainayaki and D. Yokesh

  DOI:  https://doi.org/10.37418/amsj.9.11.64

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For a graph $G$ and a proper coloring $c : V(G) \to \{1, 2, 3, \dots, k\}$ of the vertices of $G$ for some positive integer $k$, the color code of a vertex $v$ of $G$ (with respect to $c$) is the ordered $(k+1)$-tuple $code(v) = (a_0, a_1, a_2, \dots, a_k)$ where $a_0$ is the color assigned to $v$ and $1 \leq i \leq k$, $a_i$ is the number of vertices of $G$ adjacent to $v$ that are colored $i$. The coloring $c$ is irregular if distinct vertices have distinct color codes and the irregular chromatic number $\chi_{ir}(G)$ of $G$ is the minimum positive integer $k$ for which $G$ has an irregular $k$-coloring. In this paper, we obtain the values of irregular coloring for $SF(n, 1)$, friendship graph and splitting graph of star graph.

Keywords: Irregular coloring, irregular chromatic number.