Manila Journal of Science 10 (2017), pp. 16-24

A Sum Labelling for Some Families of Unicyclic Graphs

Abstract

In 2008, H. Fernau et al. provided an optimal sum labelling scheme of the generalized friendship graph and showed that its sum number is 2. The generalized friendship graph is a symmetric collection of cycles meeting at a common vertex. This graph fq,p may also be viewed as a graph obtained by considering several copies of a cycle and identifying a vertex from each cycle and merging them into a single vertex. In this paper, we consider a cycle and several paths and form a graph by concatenating a pendant vertex from a path to a vertex in the cycle. We also determine the exact value or a bound for the sum number of the resulting graph. Specifically, we show that the sum number of tadpole graph Tn,m and the graph SmCn is at most 2 and that the crown graph ckn has a 1-optimal sum labelling.

Manila Journal Of Science 10 (2017), Pp 16-24 (1.4 MiB)