On magic total labelings in combinatorial designs

Abstract

Let H be a graph and ẞ be an H-decomposition of G. The H-magic total labeling of a graph G is an assignment of integers set [1, |V(G)∪E(G)|] to V(G)∪E(G) such that: any vertex and any edge of G receive distinct integers, and the sum of all vertices receive integers and all edges receive integers on B is a constant for any B ∈ ẞ. In this paper we study the H-super magic problems of balanced incomplete block designs and resolvable balanced incomplete block designs.