# Cohen Macaulay Hybrid Graphs

## TL;DR

This paper introduces hybrid graphs, a new family of graphs, and proves their Cohen-Macaulay property, also characterizing Cohen-Macaulay chordal graphs as hybrid graphs, expanding understanding of graph properties in algebraic combinatorics.

## Contribution

The paper defines hybrid graphs, proves they are Cohen-Macaulay, and characterizes Cohen-Macaulay chordal graphs as hybrid graphs, establishing new links between graph theory and algebraic properties.

## Key findings

- Every hybrid graph associated with a given graph is Cohen-Macaulay.
- There are infinitely many hybrid graphs for each graph.
- Every Cohen-Macaulay chordal graph is a hybrid graph.

## Abstract

We introduce a new family of graphs, namely, hybrid graphs. There are infinitely many hybrid graphs associated to a single graph. We show that every hybrid graph associated to a given graph is Cohen Macaulay. Furthermore, we show that every CohenMacaulay chordal graph is a hybrid graph.