(DOWNLOAD) "Open Alliance in Graphs (Report)" by N. Jafari Rezazadeh, H. Rad # eBook PDF Kindle ePub Free
eBook details
- Title: Open Alliance in Graphs (Report)
- Author : N. Jafari Rezazadeh, H. Rad
- Release Date : January 01, 2010
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 70 KB
Description
[section] 1. Introduction In this paper we study open alliance in graphs. For graph theory terminology and notation, we generally follow [3]. For a vertex v in a graph [member of] = (V, E), the open neighborhood of v is the set N(v) = {u : uv [member of] E}, and the closed neighborhood of v is N[v] = N(v) [union] {v}. The boundary of S is the set [partial derivative]S = [[universal].sub.v[member of]S] - S. We denote the degree of v in S by [d.sub.S](v) = N(v) [intersection] S. The edge connectivity, [lambda](G), of a graph [member of] is the minimum number of edges in a set, whose removal results in a disconnected graph. A graph G' = (V', E') is a subgraph of a graph [member of] = (V, E), written G' [subset or equal to] G, if V' [subset or equal to] V and E' [subset or equal to] E. For S [subset or equal to] V, the subgraph induced by S is the graph G[S] = (S, E [intersection] S x S).
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