The irredundance number and maximum degree of a graph
Abstract
A vertex η in a subset X of vertices of an undirected graph is redundant if its closed neighborhood is contained in the union of closed neighborhoods of vertices of X-{η}. In the context of a communications network, this means that any vertex that may receive communications from X may also be informed from X-{η}. The irredundance number ir(G) is the minimum cardinality taken over all maximal sets of vertices having no redundancies. In this note we show that ir(G) ≥ n/(2Δ-1) for a graph G having n vertices and maximum degree Δ. © 1984.
Publication Title
Discrete Mathematics
Recommended Citation
Bollobás, B., & Cockayne, E. (1984). The irredundance number and maximum degree of a graph. Discrete Mathematics, 49 (2), 197-199. https://doi.org/10.1016/0012-365X(84)90118-3
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