# Odd Covers of Graphs

## Conference Year

January 2023

## Abstract

Graphs are abstractions of many networks around us: social networks or the World Wide Web, to name just a couple. For various applications, there is interest in efficiently encoding a graph for a computer. We address a problem which relates to finding a “smallest” matrix with which to encode a graph. The problem, phrased in terms of a social network, is to find the minimum number of clubs that a given group of people can form under the condition that, if two people are friends, they are in an odd number of clubs together, and otherwise in an even number.

## Primary Faculty Mentor Name

Puck Rombach

## Status

Graduate

## Student College

College of Engineering and Mathematical Sciences

## Program/Major

Mathematics

## Primary Research Category

Engineering and Math Science

Odd Covers of Graphs

Graphs are abstractions of many networks around us: social networks or the World Wide Web, to name just a couple. For various applications, there is interest in efficiently encoding a graph for a computer. We address a problem which relates to finding a “smallest” matrix with which to encode a graph. The problem, phrased in terms of a social network, is to find the minimum number of clubs that a given group of people can form under the condition that, if two people are friends, they are in an odd number of clubs together, and otherwise in an even number.