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2017•arXiv (Cornell University)Open access

A Coordinate System for Graphs

Ameneh Farhadian

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Abstract

In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes of $n$-vertex graphs. Using dot product of graphs, a coordinate system for graphs is provided which benefits us in graph isomorphism and related problems.

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What this paper is about

In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes of $n$-vertex graphs. Using dot product of graphs, a coordinate system for graphs is provided which benefits us in graph isomorphism and related problems.

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Available abstract

In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes of $n$-vertex graphs. Using dot product of graphs, a coordinate system for graphs is provided which benefits us in graph isomorphism and related problems.

Key concepts: Graph isomorphism, Combinatorics, Graph product, Mathematics, Isomorphism (crystallography), Discrete mathematics, Vertex (graph theory), Graph

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