On the girth and diameter of generalized Johnson graphs

Let v > k > i be non-negative integers. The generalized Johnson graph, J(v, k, i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever vertical bar A boolean AND B vertical bar = i. In this article, we derive general formulas for the girth and diameter of J(v, k, i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection. (C) 2017 Elsevier B.V. All rights reserved.