Abstract
A (p, q)-graph G is said to be (1, N)-arithmetic if there is a function from the vertex set V(G) to
so that the values obtained as the sums of the labeling assigned to their end vertices, can be arranged in the arithmetic progression
. In this paper, we prove that Stars, Paths, complete bipartite graph
, highly irregular graph
and Cycle
are (1, N)-arithmetic,
is not (1, N)-arithmetic. We also prove that no graph G containing an odd cycle is (1, N)-arithmetic for every positive integer N.
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