# A Coordinate System for Graphs

## TL;DR

This paper introduces a novel coordinate system for graphs based on a dot product-like function, facilitating graph isomorphism analysis and related problems by defining orthogonality and a new metric on graph classes.

## Contribution

It proposes a new graph coordinate system using a dot product-like function, advancing methods for graph isomorphism and graph comparison.

## Key findings

- Defines a graph function similar to dot product
- Introduces graph orthogonality and a new metric
- Provides a coordinate system for graphs

## 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.