On Delta Graphs and Delta Conjecture

TL;DR

This paper introduces two families of graphs, proves the delta conjecture for one, and explores their properties and relationships with minimum semidefinite rank.

Contribution

It defines C-delta and delta graphs, proves the delta conjecture for delta graphs, and analyzes their relationship with minimum semidefinite rank.

Findings

Delta graphs satisfy the delta conjecture.

C-delta graphs can be identified as complements of delta graphs.

A list of C-delta graphs and their minimum semidefinite rank relationships.

Abstract

In this paper we define two infinite families of graphs called C-$\delta$ graphs and $\delta$- graph and prove that $\delta$-graphs satisfy $\delta$ conjecture. Also we introduce a family of C-$\delta$ graphs from which we can identify $\delta$ graphs as their complements. Finally we give a list of C-$\delta$ graphs and the relationship with their minimum semidefinite rank.