Original scientific paper

https://doi.org/10.25027/agj2017.28.v30i3.190

(1, N ) - Arithmetic Labelling of Arbitrary Supersubdivision of disconnected graphs

Ramachandran Varatharaja Perumal orcid.org/0000-0001-7341-7278 ; Department of Mathematics, Mannar Thirumalai Naicker College, Madurai, Tamil Nadu, India
Anubala Sekar ; Department of Mathematics, VPMM College of Arts and Science for Women, Krishnankovil, Tamil Nadu, India

Abstract

A (p, q) -graph G is said to be (1, N ) -Arithmetic if there is a function φ from the vertex set V (G) to {0, 1, N, (N + 1), 2N, (2N + 1), . . . , N (q − 1), N (q − 1) + 1} so that the values obtained as the sums of the labelling assigned to their end vertices, can be arranged in the arithmetic progression {1, N + 1,
2N + 1, . . . , N (q − 1) + 1} . In this paper we prove that the arbitrary supersubdivision of disconnected paths Pn U Pr and disconnected path and cycle Pn U Pr are (1, N ) -Arithmetic Labelling for all positive integers N > 1 .

Keywords

(1, N ) -Arithmetic Labelling, Supersubdivisions, Arbitrary supersubdivision, dis- connected paths, disconnected path and cycle.

Hrčak ID:

274648

URI

https://hrcak.srce.hr/274648

Publication date:

31.3.2022.

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