#### Title

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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#### Recommended Citation

Lapus, R. R. (2007). The aggregate of a graph. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/7819

#### Disciplines

Mathematics

#### Keywords

Graph theory

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