2019/01/22 by S. Morteza Mirafzal, Mirafzal, S. Morteza, A. Heidari +1 · 1 citation
Computer Science · Engineering · #Advanced Graph Theory Research #Interconnection Networks and Systems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1901.07207
For any given n,m ∈ ℕ with m < n , the Johnson graph J(n,m) is defined as the graph whose vertex set is V=\v| v⊆ [n]=\1,...,n\, |v|=m\, where two vertices v,w are adjacent if and only if |v∩ w|=m-1. A graph G of order n > 2 is panconnected if for every two vertices u and v, there is a u-v path of length l for every integer l with d(u,v) ≤ l ≤ n-1. In this paper, we prove that the Johnson graph J(n,m) is a panconnected graph.