On Mod(3)-Edge-Magic Graphs

Abstract

Let G be a (p, q)-graph in which the edges are labeled 1, 2, . . . , q. The vertex sum for a vertex v is the sum of the labels of the incident edges at v. If the vertex sums are constant, modulo k, where k>= 2, then G is said to be Mod(k)-edge-magic. When k = p, Mod(p)-edge-magic graph is the edge-magic graph which was introduced by the Lee, Seah and Tan in [9]. In this paper we investigate graphs which are Mod(3)-edge-magic.DOI : http://dx.doi.org/10.22342/jims.0.0.81.

Arithmetic Progression Graphs

“…Gallian's updated survey [4] is a comprehensive reference on the subject, see also [12,11]. Among the most studied methods of graph labeling we mention magic labeling [6], edge magic labeling [7], graceful labeling [9,3], (k, d)-arithmetic labeling [1], and super edge-antimagic labeling [2]. In these types of labeling the mapping and its domain are very restricted and few graphs accept those kinds of labelings.…”