A Class of Degree-Magic Join Graphs

Abstract

A graph is called degree-magic if it admits a labelling of the edges by integers \(\{1, 2, \ldots, |E(G)|\}\) such that the sum of the labels of the edges incident with any vertex \(v\) is equal to \(\left(1 + |E(G)|\right)/2 \deg(v)\). In this paper, we show that a class of join graphs are degree-magic.