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 |A ∩ B| = 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.
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