%A Varatharaja Perumal, Ramachandran
%A Sekar, Anubala
%D 2022
%T (1, N)-Arithmetic Labelling of Arbitrary Supersubdivision of disconnected graphs
%K
%X 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.
%U https://actagraphica.hr/index.php/actagraphica/article/view/190
%J Acta Graphica
%0 Journal Article
%R 10.25027/agj2017.28.v30i3.190
%P 25-31
%V 30
%N 3
%@ 1848-3828
%8 2022-03-31