Some Important Results on Triangular Sum Graphs
Samir K. VAIDYA, Udayan M. Prajapati · 2009
Let G =( V,E) be a graph with p vertices an q edges. A graph G is said to admit a triangular sum labeling if its vertices can be labeled by non-negative integers such that induced edge labels obtained by the sum of the labels of end vertices are the first q triangular numbers. A graph G which admits a triangular sum labeling is called a triangular sum graph. In the present work we investigate some classes of graphs which does not admit a triangular sum labeling. Also we show that some classes of graphs can be embedded as an induced subgraph of a triangular sum graph. This work is a nice composition of graph theory and combinatorial number theory.