A Note on Chromatic Sum
Meysam Alishahi, Ali Taherkhani

TL;DR
This paper explores properties of the chromatic sum of graphs, providing a necessary condition for graph homomorphisms and establishing an inequality relating the chromatic sum to the fractional chromatic number and the size of the graph.
Contribution
It introduces a necessary condition for the existence of graph homomorphisms and proves an inequality linking the chromatic sum with fractional chromatic number and graph order.
Findings
Established a necessary condition for graph homomorphisms.
Proved that the chromatic sum is less than the product of fractional chromatic number and graph size.
Abstract
The chromatic sum of a graph 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 for every graph .
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
