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Universal minimal total dominating functions in graphs

โœ Scribed by E. J. Cockayne; C. M. Mynhardt; Bo Yu


Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
544 KB
Volume
24
Category
Article
ISSN
0028-3045

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๐Ÿ“œ SIMILAR VOLUMES


Universal minimal total dominating funct
โœ Alan Stacey ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 179 KB

We show that any tree that has a universal minimal total dominating function has one which only takes 0-1 values. K 3 demonstrates that this fails for graphs in general. Given a graph G =(V, E), for each vertex ve V let F(v) be the set of its neighbours (in particular, not including v itself). A to

Convexity of minimal total dominating fu
โœ Yu, Bo ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 122 KB ๐Ÿ‘ 2 views

A total dominating function (TDF) of a graph G = (V, E) is a function f : V โ†’ [0, 1] such that for each v โˆˆ V , the sum of f values over the open neighbourhood of v is at least one. Zero-one valued TDFs are precisely the characteristic functions of total dominating sets of G. We study the convexity

A characterisation of universal minimal
โœ E.J. Cockayne; C.M. Mynhardt ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 445 KB

A total dominating function (TDF) of a graph G = (V, E) is a function f: V~ [0, 1] such that for each v~ V, ~u~Ntv)f(u)>~ 1, where N(v) denotes the set of neighbours of v. Although convex combinations of TDFs are also TDFs, convex combinations of minimal TDFs (MTDFs) are not necessarily minimal. An

Total dominating functions in trees: Min
โœ E. J. Cockayne; C. M. Mynhardt; Bo Yu ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 380 KB

## Abstract A total dominating function (TDF) of a graph __G__ = (__V, E__) is a function __f__: __V__ โ† [0, 1] such that for each __v__ ฯต V, ฮฃ~uฯตN(v)~ f(u) โ‰ฅ 1 (where __N__(__v__) denotes the set of neighbors of vertex __v__). Convex combinations of TDFs are also TDFs. However, convex combinations

Total domination in graphs
โœ E. J. Cockayne; R. M. Dawes; S. T. Hedetniemi ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 374 KB
Total domination in block graphs
โœ Gerard J Chang ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 382 KB