## Abstract We prove a conjecture of Favaron et al. that every graph of order __n__ and minimum degree at least three has a total dominating set of size at least __n__/2. We also present several related results about: (1) extentions to graphs of minimum degree two, (2) examining graphs where the bo
Some remarks on domination in cubic graphs
β Scribed by Bohdan Zelinka
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 445 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We study three recently introduced numerical invariants of graphs, namely, the signed domination number y., the minus domination number 7 and the majority domination number ymaj. An upper bound for ys and lower bounds for ;'-and Y,,~ are found, in terms of the order of the graph.
π SIMILAR VOLUMES
Our purpose is to consider the following conjectures: Conjecture 1 (Barneffe). . Every cubic 3-connected bipartite planar graph is Hamiltonian. Conjecture 2 (Jaeger). Every cubic cyclically 4-edge connected graph G has a cycle C such that G -V(C) is acyclic. Conjecture 3 (Jackson, Fleischner). Ever
## Abstract A subset __S__ of vertices of a graph __G__ is __k__βdominating if every vertex not in __S__ has at least __k__ neighbors in __S__. The __k__βdomination number $\gamma\_k(G)$ is the minimum cardinality of a __k__βdominating set of __G__. Different upper bounds on $\gamma\_{k}(G)$ are kn