Abstract
In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area
Highlights
In this paper the linear representation of a graph is defined
Each list describes the set of neighbours of a vertex in the graph. (See [3])
An automorphism of a graph G is an isomorphism between G and itself
Summary
Abstract: In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of GL(p, R), the group of invertible matrices of order p and real coefficients. For the representation of graphs, adjacency matrix, incidence matrix and Adjacency list are used. The latter, is a collection of unordered lists used to represent a finite graph. Each list describes the set of neighbours of a vertex in the graph. A graph G is a finite nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of G called edges.
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