|
|
Article: The study of [sigma]--index on [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] graphs.(Report)
- Article from:
- Scientia Magna
- Article date:
- December 1, 2008
- Author:
CopyrightCOPYRIGHT 2008 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
|
[section] 1. Introduction
Let G = (V, E) be a simple connected graph with the vertex set V(G) and the edge set E(G). For any [upsilon] [member of] V, [N.sub.G]([upsilon]) = {u | u[upsilon] [member of] E(G)} denotes the neighbors of [upsilon], and [d.sub.G]([upsilon]) =| [N.sub.G]([upsilon]) | is the degree of [upsilon] in G; [N.sub.G][[upsilon]] = {[upsilon]} [union] [N.sub.G]([upsilon]). A leaf is a vertex of degree one and a stem is a vertex adjacent to at least one leaf. Let E' [subset equal to] E(G), we denote by G - E' the subgraph of G obtained by deleting the edges of E'. W [subset equal to] V(G), G - W denotes the subgraph of G obtained by deleting the ...