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Universal minimal total dominating functions in graphs
Author(s) -
Cockayne E. J.,
Mynhardt C. M.,
Yu Bo
Publication year - 1994
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230240205
Subject(s) - combinatorics , graph , mathematics , vertex (graph theory) , regular polygon , function (biology) , discrete mathematics , geometry , evolutionary biology , biology
A total dominating function (TDF) of a graph G = ( V, E ) is a function f : V → [0, 1] such that for each ν ϵ V , Σ uϵN(v) f(u) ⩾ 1 [where N(v) denotes the open neighborhood of vertex v ]. Integer‐valued TDFs are precisely characteristic functions of total dominating sets of G . Convex combinations of two TDFs are themselves TDFs but convex combinations of minimal TDFs (MTDFs) are not necessarily minimal. This paper is concerned with the existence of a universal MTDF in a graph, i.e., a MTDF g such that convex combinations of g and any other MTDF are themselves minimal. © 1994 by John Wiley & Sons, Inc.