Further results on relaxed mean labeling. (English) Zbl 1367.05184

Balaji, V.; Ramesh, D. S. T.; Sudhakar, S.

Int. J. Adv. Appl. Math. Mech. 3, No. 3, 92-99 (2016).

Summary: In this paper further results on relaxed mean labeling is discussed. The condition for a graph to be relaxed mean is that \(p=q+1\). We prove, the following theorems to study path, star and the characterization for the relaxed mean labeling of two star. We prove that the disjoint union of any path with \(n-1\) edges joining the pendent vertices of distinct paths is a relaxed mean graph and \(K_{1,m}\) is not a relaxed mean graph for \(m \geqslant 5\). Also, we prove that the two star \(G=(K_{1,m} \cup K_{1,n})\) with an edge in common is a relaxed mean graph if and only if \(|m-n| \leqslant5\).

MSC:

05C78

Graph labelling (graceful graphs, bandwidth, etc.)

Keywords:

relaxed mean graph; path and star