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Factor domination in graphs

✍ Scribed by Robert C. Brigham; Ronald D. Dutton


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
656 KB
Volume
86
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


Given a factoring of a graph, the factor domination number yr is the smallest number of nodes which dominate all factors. General results, mainly involving bounds on yr for factoring of arbitrary graphs, are presented, and some of these are generalizations of well known relationships.

The special case of two-factoring K, into a graph G and its complement E receives special emphasis.


πŸ“œ SIMILAR VOLUMES


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This paper generalizes dominating and efficient dominating sets of a graph. Let G be a graph with vertex set V(G). If f: V(G) ~ Y, where Y is a subset of the reals, the weight off is the sum of f(v) over all ve V(G). If the closed neighborhood sum off(v) at every vertex is at least 1, thenfis called

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In a graph G Γ… (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then ''domination'' requires every vertex to be protected. Thus, S ʚ V (G) is a dominating set if ʜ s √ S N[s] Γ… V (G). For total domination, eac

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## Abstract Let __G__ = (__V, E__) be a connected graph. A set __D__ βŠ‚ __V__ is a __set‐dominating set__ (sd‐set) if for every set __T__ βŠ‚ __V__ βˆ’ __D__, there exists a nonempty set __S__ βŠ‚ __D__ such that the subgraph γ€ˆ__S__ βˆͺ __T__〉 induced by __S__ βˆͺ __T__ is connected. The set‐domination number

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✍ E. J. Cockayne; R. M. Dawes; S. T. Hedetniemi πŸ“‚ Article πŸ“… 1980 πŸ› John Wiley and Sons 🌐 English βš– 374 KB
Majority domination in graphs
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A two-valued function f defined on the vertices of a graph G =(V, E), f: V ~I-1, 1}, is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. That is, for at least half the vertices ve V, f (N[v])~ 1, where N [ v ] consists of v

Domination-balanced graphs
✍ Charles Payan; Nguyen Huy Xuong πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 355 KB

## Abstract A set __D__ of vertices in a graph is said to be a dominating set if every vertex not in __D__ is adjacent to some vertex in __D.__ The domination number Ξ²(__G__) of a graph __G__ is the size of a smallest dominating set. __G__ is called domination balanced if its vertex set can be part