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
Universal minimal total dominating functions in graphs
โ 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
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A total dominating function (TDF) of a graph G = (V, E) is a function f : V โ [0, 1] such that for each v โ 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 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
## 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) โฅ 1 (where __N__(__v__) denotes the set of neighbors of vertex __v__). Convex combinations of TDFs are also TDFs. However, convex combinations