International Journal of Pure and Applied Mathematics Volume 120 No. 3 2018, 487-496 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v120i3.16 P A ijpam.eu EDGE TRIMAGIC GRACEFUL LABELING OF GRAPHS M. Regees 1 , J.A. Jose Ezhil 2 § , T. Shyla Isac Mary 3 1 Department of Mathematics Malankara Catholic College Mariagiri, Kaliakavilai - 629153, Tamilnadu, INDIA 2 Department of Mathematics Nesamony Memorial Christian College Marthandam-629165,Tamilnadu, INDIA 3 Department of Mathematics Nesamony Memorial Christian College Marthandam-629165,Tamilnadu, INDIA Abstract: A(p, q) graph G is called edge trimagic total if there exists a bijection f : V (G) ∪ E(G) →{1, 2, 3, ..., p + q} such that for each edge xy in E(G) the value of f (x)+ f (xy)+ f (y)= K1 or K2 or K3. G is called edge trimagic graceful if there exists a bijection f : V (G) ∪ E(G) →{1, 2, 3, ..., p + q} such that for each edge xy in E(G), |f (x) − f (xy)+ f (y)| = c1 or c2 or c3, where c1, c2, and c3 are constants. In this paper, we introduce edge trimagic graceful labeling of some graphs and proved that the square graph P 2 n ,(Pn; S1) and the comp Pn ⊙ K1 are edge trimagic graceful graphs. AMS Subject Classification: 05C78 Key Words: graph, labeling, magic, trimagic 1. Introduction Let G be a simple, undirected graph with n vertices. Let V (G) and E(G) denote the vertex set and the edge set of the graph G, respectively. Labeling of Received: October 25, 2017 Revised: January 13, 2018 Published: January 14, 2018 c  2018 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author