On Opinionated Complete Bipartite Graphs

Laura Parrish

fantasticasognatrice@yahoo.com

Joint work with

and

June 18, 2013

Abstract

Letâ€™s a have a bipartite complete graph and call it G. Because such

graph is bipartite, it has two sets of vertices called respectively set V (G)

and set U (G), and the set constituted by its edges is called E(G). Any

edges e is adjacent to a vertex v(V ) and to a vertex u(U ), and, since

the graph is bipartite (so it has two subsets of vertices) no vertex is adjacent to any vertex of its same set. Since the graph is complete, every

vertex v is adjacent to every vertex u, and every vertex u is adjacent to

every vertex v. A vertex is called opinionated if the algebraic difference

between the total number of its incident edges labeled 1, and the total

number of its incident edges labeled 0, is equal zero. We call a graph

G edge-friendly if the algebraic difference between the total number of

its incident edges labeled 1 and the total number of its incident edges labeled 0 is equal zero.We show an algorithm that for every positive integers

n, m, of the graph Kn,m guarantees to make the graph opinionated and

edge-friendly.

The label 1 is represented by the color red, and the label 0 is represented by the color black

1

Introduction

While working with bipartite complete graph, our goal is to keep the graph

opinionated and edge-friendly. Since the bipartite graphs do not offer clarity in

their vision, and most, if they are large, we need to be able to represent them

graphically in a more efficient way.

We are going to represent them using a matrix.

Because the upper vertices of the bipartite graph constitute the set V , and

all the down vertices constitute the set U of the graph K( n, n), we need to

represent graphically the 2 sets: {v1 ,v2 ,v3 ,vn } and {u1 ,u2 ,u3 ,un }.

When all the adjacent edges to the first upper vertex v1 to the down vertices

u1 ,u2 ,u3 ,un are reported in the first row of...

- Graph Interpretation
- graph describe
- Climate Graph
- Scatter Graphs
- graph description
- Graphs About Prison Overcrwoding
- Definition of graph theory
- Facebook: Building a Business from the Social Graph
- Reliable graph based routing in vanet environment
- QNT 273 Week 2 Learning Team Assignment Misleading Graphs Paper