2021/04/19 by C. M. Mynhardt, A. Roux, Mynhardt, C. M. +1
Computer Science · Engineering · Mathematics · #05C69 #Advanced Graph Theory Research #Cardinality (data modeling) #Combinatorics #Combinatorics (math.CO) #Computer science #Discrete mathematics #Disjoint sets #FOS: Mathematics #Graph #Graph Labeling and Dimension Problems #Mathematics #Neighbourhood (mathematics) #Vertex (graph theory) #graph theory and CDMA systems #math.CO #msc:05C69
paper · pdf · doi:10.48550/arxiv.2104.09004
published in arXiv (Cornell University) (Cornell University) · 16 pages, 6 figures
openalex publication_date 2021/04/19 · arxiv created 2021/04/23 · arxiv updated 2021/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A set D of vertices of a graph G with vertex set V is irredundant if each non-isolated vertex of G[D] has a neighbour in V-D that is not adjacent to any other vertex in D. The upper irredundance number IR(G) is the largest cardinality of an irredundant set of G; an IR(G)-set is an irredundant set of cardinality IR(G). The IR-graph of G has the IR(G)-sets as vertex set, and sets A and B are adjacent if and only if B can be obtained from A by exchanging a single vertex of A for an adjacent vertex in B. An IR-tree is an IR-graph that is a tree. We characterize IR-trees of diameter 3 by showing that these graphs are precisely the double stars S(2n,2n), i.e., trees obtained by joining the central vertices of two disjoint stars K1,2n.