An independent set C of vertices in a graph is an e cient dominating set (or perfect code) when each vertex not in C is adjacent to exactly one vertex in C. An E-chain is a countable family of nested graphs, each of which has an e cient dominating set. The Hamming codes in the n-cubes provide a clas
Efficient open domination in Cayley graphs
โ Scribed by T. Tamizh Chelvam; Sivagnanam Mutharasu
- Book ID
- 116217528
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 230 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube __Q~n~__ has an independent perfect domination set if and only if __Q~n~__ i
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
A set \(S\) of vertices of a graph \(G\) is called an efficient open domination set for \(G\) if the set of neighborhoods \(\{N(v) \mid v \in S\}\) forms a partition of \(V(G)\). A graph is an efficient open domination graph if it contains an efficient open domination set. Several properties of effi