The Cohen-Macaulay type of edge-weighted r-path ideals

TL;DR

This paper provides a combinatorial method to determine the Cohen-Macaulay type of edge-weighted r-path suspensions of graphs, generalizing the case of r=1, with implications for algebraic graph theory.

Contribution

It introduces a combinatorial approach to compute the Cohen-Macaulay type for edge-weighted r-path suspensions, extending previous results for r=1.

Findings

Combinatorial description of Cohen-Macaulay type for r-path suspensions.

Generalization of Cohen-Macaulay type computation from r=1 to arbitrary r.

Simplification of calculations for specific classes of edge-weighted graphs.

Abstract

We describe combinatorially the Cohen-Macaulay type of edge-weighted r-path suspensions of edge-weighted graphs for an arbitrary positive integer r. The computation of the Cohen-Macaulay type of edge-weighted suspensions of edge-weighted graphs becomes a special case of r = 1.