%0 Journal Article %T On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Rahimi Sharbaf, S. %A Erfani, Kh. %D 2017 %\ 02/01/2017 %V 4 %N 1 %P 33-42 %! On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs %K ‎edge-difference chromatic sum‎ %K ‎edge-sum chromatic sum‎ %K ‎graph homomorphism‎ %K ‎Kneser graph‎ %K ‎fractional chromatic number %R 10.22034/as.2017.1066 %X ‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$\sum_c D(G)=\sum |c(a)-c(b)|$ and $\sum_s S(G)=\sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $ab\in E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $\sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $\sum S(G)$‎, ‎are respectively the minimum possible values‎ ‎of $\sum_c D(G)$ and $\sum_c S(G)$‎, ‎where the minimums are taken over all proper coloring of $c$‎. ‎In this work‎, ‎we study the edge-difference chromatic sum and the edge-sum chromatic sum of graphs‎. ‎In this regard‎, ‎we present some necessary conditions for the existence of homomorphism between two graphs‎. ‎Moreover‎, ‎some upper and lower bounds for these parameters in terms of the fractional chromatic number are introduced‎ ‎as well‎. %U https://as.yazd.ac.ir/article_1066_632a2cc0dfa501dfe96f93a086cd2645.pdf