TY - JOUR
AU - Varatharaja Perumal, Ramachandran
AU - Sekar, Anubala
PY - 2022/03/31
TI - (1, N)-Arithmetic Labelling of Arbitrary Supersubdivision of disconnected graphs
JF - Acta Graphica; Vol 30 No 3 (2019)DO - 10.25027/agj2017.28.v30i3.190
KW -
N2 - 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.
UR - https://actagraphica.hr/index.php/actagraphica/article/view/190