On the strongly c-harmoniousness of cycle with 2 consecutive chords

Abstract

Let C_n(i;a, b) denotes the n-cycle with consecutive vertices x₁,x₂,...,x_n to which the 2 chords x _ix_a,x_ix_b have been added. Gallian [7] surveyed the results on harmonious labelling and strongly c-harmonious labelling of graphs and posed the problem whether the cycle C_n with k consecutive chords is harmonious or not. In this paper, we prove that the graph C_n(i;a,a + 1) is strongly c-harmonious for any integer n ≥ 5. This implies that the cycle C_n with 2 consecutive chords is harmonious.