Semester
Fall
Date of Graduation
2003
Document Type
Thesis
Degree Type
MS
College
Statler College of Engineering and Mineral Resources
Department
Lane Department of Computer Science and Electrical Engineering
Committee Chair
Elaine M. Eschen.
Abstract
Let G be an undirected graph, A be an (additive) abelian group and A* = A - {lcub}0{rcub}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V(G ) A satisfying Sv∈VG b(v) = 0, there is a function f : E(G) A* such that at each vertex v ∈ V(G), ∂f(v), the net flow out from v, equals b( v). An A-nowhere-zero-flow (abbreviated as A-NZF) in G is a function f : E(G) A* such that at each vertex v ∈ V(G), ∂f(v) = 0.;In this paper, we investigate the group connectivity number Lambda g(G) = min{lcub}n : if A is an abelian group with |A| ≥ n, then G is A-connected{rcub} for certain families of graphs including complete bipartite graphs, chordal graphs, wheels and biwheels. We also give some general results and methods to approach nowhere zero flow and group connectivity problems.
Recommended Citation
Chen, Jingjing, "Generalized nowhere zero flow" (2003). Graduate Theses, Dissertations, and Problem Reports. 1367.
https://researchrepository.wvu.edu/etd/1367