Total dominating functions in trees: Minimality and convexity | Zendy

Cockayne E. J. | Zendy; Mynhardt C. M. | Zendy; Yu Bo | Zendy

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Total dominating functions in trees: Minimality and convexity

Author(s) -

Cockayne E. J.,

Mynhardt C. M.,

Yu Bo

Publication year - 1995

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190190109

Subject(s) - combinatorics , mathematics , convexity , graph , vertex (graph theory) , regular polygon , function (biology) , convex function , geometry , evolutionary biology , financial economics , economics , biology

A total dominating function (TDF) of a graph G = ( V, E ) is a function f : V ← [0, 1] such that for each v ϵ V, Σ uϵN(v) f(u) ≥ 1 (where N ( v ) denotes the set of neighbors of vertex v ). Convex combinations of TDFs are also TDFs. However, convex combinations of minimal TDFs (i.e., MTDFs) are not necessarily minimal. In this paper we discuss the existence in trees of a universal MTDF (i.e., an MTDF whose convex combinations with any other MTDF are also minimal). © 1995 John Wiley & Sons, Inc.

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