## Universal minimal total dominating functions in graphs.(English)Zbl 0804.90122

Summary: A total dominating function (TDF) of a graph $$G= (V,E)$$ is a function $$f: V\to [0,1]$$ such that for each $$v\in V$$, $$\sum_{u\in N(v)}f(u)\geq 1$$ [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.

### MSC:

 90C35 Programming involving graphs or networks
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### References:

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