- Title
- The convexity graph of minimal total dominating functions of a graph
- Creator
- Arumugam, S.; Jerry, Sithara
- Relation
- Kragujevac Journal of Mathematics Vol. 36, Issue 1, p. 119-131
- Publisher
- Faculty of Science, University of Kragujevac
- Resource Type
- journal article
- Date
- 2012
- Description
- Let G = (V;E) be a graph without isolated vertices. A function f: V→[0; 1] is a total dominating function if [formula cound not be replicated]. A total dominating function f is called a minimal total dominating function (MTDF) if any function g: V→[0; 1] with g < f is not a total dominating function. If f is an MTDF of G, then Pf={v ∈ V: f(v) > 0} is the positive set of f and is the boundary set of f. The relation P defined on the set F of all MTDFs of G by fpg if Pf = Pg and Bf = Bg is an equivalence relation which partitions F into a finite number of equivalence classes X1, X2,... Xt. The total convexity graph CT (G) of G has {X1, X2,...Xt} as its vertex set and Xi is adjacent to Xj if there exist f ∈ Xi and g ∈ Xj such that any convex combination of f and g is an MTDF of G. In this paper we determine the total convexity graphs of some standard graphs.
- Subject
- total dominating function; minimal total dominating function; total convexity graph
- Identifier
- http://hdl.handle.net/1959.13/1336737
- Identifier
- uon:27689
- Identifier
- ISSN:1450-9628
- Language
- eng
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