The e-mail gossip number and the connected domination number
โ Scribed by F. Harary; B. Raghavachari
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 184 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
โฆ Synopsis
Our
object is to introduce eg(G), the e-mail gossip number of a connected graph G, and derive a simple equation expressing this new invariant in terms of the known [1] connected domination number cd(G). As a corollary we see that determining each of these numbers is NP-hard. In general we follow the graph theoretic notation and terminology of [2]. Throughout G = (V, E) is a connected graph with IV] = n nodes.
๐ SIMILAR VOLUMES
The closed neighborhood of a vertex subset S of a graph G = (V,E), denoted as N[Sj, is defined ss the union of S and the set of all the vertices adjacent to some vertex of S. A dominating set of a graph G = (V, E) is defined as a set S of vertices such that N[q = V. The domination number of a graph
Let ฮณ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43-56] and Bollobรกs and Cock- ayne [J. Graph Theory (1979) 241-249] proved independently that ฮณ(G) < 2ir(G) for
Upper bounds for u + x and ax are proved, where u is the domination number and x the chromatic number of a graph.
## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^โ1^) = __n__^nโ2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp
A dominatin# set for a graph G = (V, E) is a subset of vertices V' c\_ V such that for all v โข V-V' there exists some uโข V' for which {v,u} โขE. The domination number of G is the size of its smallest dominating set(s). For a given graph G with minimum size dominating set D, let mz(G, D) denote the nu