A Note on Chromatic Sum
classification
🧮 math.CO
keywords
graphchromaticsigmacoloringcolorsconditioneveryexistence
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The chromatic sum $\Sigma(G)$ of a graph $G$ is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present $\Sigma(G)<\chi_f(G)|G|$ for every graph $G$.
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