Title: The graph SSG(2) is odd graceful and odd harmonious

Authors: J. Jeba Jesintha; K. Ezhilarasi Hilda Stanley

Addresses: PG Department of Mathematics, Women's Christian College, Chennai, India ' Department of Mathematics, Ethiraj College for Women, Chennai, India

Abstract: A subdivided shell graph is obtained by subdividing the edges in the path of the shell graph. Let G₁, G₂, G₃, ..., G_n be 'n' subdivided shell graphs of any order. The graph SSG(n) is obtained by adding an edge to apexes of G_i and G_i+1, i = 1, 2, ..., (n−1). The graph SSG(n) is called a path union of 'n' subdivided shell graphs of any order. In this paper we prove that the subdivided shell graph is odd harmonious. We also prove that SSG(n) is odd graceful and odd harmonious when n = 2.

Keywords: odd graceful labelling; odd harmonious labelling; subdivided shell graph; SSG(2); graceful labelling; harmonious labelling; shell graph.

DOI: 10.1504/IJCAET.2021.111639

International Journal of Computer Aided Engineering and Technology, 2021 Vol.14 No.1, pp.93 - 101

Accepted: 17 Jul 2018
Published online: 07 Dec 2020 *

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