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

Graph Theory

  • Ramachandran Varatharaja Perumal Mannar Thirumalai Naicker College
  • Anubala Sekar

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 ∪Pr and disconnected path and cycle Pn∪C r  are (1, N) -Arithmetic Labelling for all positive integers N > 1.

Published
Mar 31, 2022
How to Cite
VARATHARAJA PERUMAL, Ramachandran; SEKAR, Anubala. (1, N)-Arithmetic Labelling of Arbitrary Supersubdivision of disconnected graphs. Acta Graphica, [S.l.], v. 30, n. 3, p. 25 - 31, mar. 2022. ISSN 1848-3828. Available at: <https://actagraphica.hr/index.php/actagraphica/article/view/190>. Date accessed: 11 aug. 2022. doi: http://dx.doi.org/10.25027/agj2017.28.v30i3.190.
Section
Original Scientific Papers