Gracefulness of the Join of Graceful Graph and -P_k-
Luthfan Fawwaz, Mohammad Farhan, Tasnim Bilal, Denny Riama Silaban

Universitas Indonesia

Abstract

Given a graceful graph -G- with order -n- and size -m- and -P_k- is a path graph with -k- vertices. We discuss the gracefulness of the join of -G- and -P_k-, denoted by -G+P_k-. Firstly, we show that if -n=m+1- then -G+P_2- is a graceful graph. Furthermore, we found some sufficient condition for the join of -G+P_k-. Lastly, we prove that for -k=3,5,7-, -G+P_k- are also graceful.

Keywords: Graceful Graph-Path Graph-Labeling

Topic: Mathematics