A Family of Integral Sum Graphs
Jingzi Li · Journal of Qufu Normal University · 2007
A graph G is said to be an integral sum graph if its points can be given a labeling f with distinct integers,such that for any two distinct points u,v∈G,uv is an edge of G if and only if f(u)+f(v)=f(w) for some point w of G.A graph is said to be a(*)-sum graph if it has no point which is adjacent to other points of the graph,and it has an integral sum labeling which has a negative integral label and a sole point which absolute value is maximum.A generalized star is obtained from a star by extending each edge to a path.In this paper,a new family of graphs-(*)-sum graph identified with a generalized star-is discussed and proved to be integral sum graphs.