Arithmetic graphs
B. Devadas Acharya, S. M. Hegde · Journal of Graph Theory · 1990
Abstract A (p, q)‐graph G is said to be (k, d)‐arithmetic if its vertices can be assigned distinct nonnegative integers so that the values of the edges, obtained as the sums of the numbers assigned to their end vertices, can be arranged in the arithmetic progression k, k + d, k + 2d, …, k + (q ‐ 1)d. In this paper we initiate a study on the structures of finite (k, d)‐arithmetic graphs.