The aggregate of a graph

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Archival Material/Manuscript

Publication Date

10-2007

Abstract

Let G = (V, E) be a finite, undirected graph containing no loops nor multiple edges, where V is the vertex set with N points/vertices and E is the edge set containing M lines. The token of the edge e in G is the number of neighboring edges of e while the aggregate of G, denoted by v(G), is the sum of the each token of e ∈ E. The notion of the rational weight of G by Guerrero, Guerrero and Artes is the sum of the degree vertices in G divided by the order of G.

This paper investigates the properties of the graph parameter v(G) and illustrates this concept to some special classes of graphs, such as: paths, cycles, fans, wheel graphs, bipartite graphs, complete graphs and trees. In addition, this paper studies the relationship of v(G) to the aggregate and rational weight of the line graph of G. Furthermore, the calculation of the aggregate of a newly generated graph from the old ones through join and product operations.

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Disciplines

Mathematics

Keywords

Graph theory

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