TY - JOUR ID - 1066 TI - On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Rahimi Sharbaf, S. AU - Erfani, Kh. AD - School of Mathematical Science, Shahrood University of Technology, Shahrood, Iran. Y1 - 2017 PY - 2017 VL - 4 IS - 1 SP - 33 EP - 42 KW - ‎edge-difference chromatic sum‎ KW - ‎edge-sum chromatic sum‎ KW - ‎graph homomorphism‎ KW - ‎Kneser graph‎ KW - ‎fractional chromatic number DO - 10.22034/as.2017.1066 N2 - ‎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. UR - https://as.yazd.ac.ir/article_1066.html L1 - https://as.yazd.ac.ir/article_1066_632a2cc0dfa501dfe96f93a086cd2645.pdf ER -