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Let $\mathcal{C} = \{c_1,c_2, c_3, \ldots,c_k\}$ be a certain type of proper$k$-colouring of a given graph $G$ and $\theta(c_i)$ denote the number of timesa particular colour $c_i$ is assigned to the vertices of $G$. Then, thecolouring sum of a given graph $G$ with respect to the colouring $\cC$, denotedby $\omega_{\cC}(G)$, is defined to be $\omega(\cC) =\sum\limits_{i=1}^{k}i\,\theta(c_i)$. The colouring sums such as$\chi$-chromatic sum, $\chi^+$-chromatic sum, $b$-chromatic sum,$b^+$-chromatic sum etc. are some of these types of colouring sums that havebeen studied recently. Motivated by these studies on certain chromatic sums ofgraphs, in this paper, we study certain chromatic sums for some standard cyclerelated graphs.

Certain Chromatic Sums of Some Cycle Related Graph Classes