Computational aspects of line simplicial complexes

Article type: Research Article

Authors: Ahmed, Imran^{; *} | Muhmood, Shahid

Affiliations: Department of Mathematics, COMSATS University Islamabad - Lahore Campus, Lahore, Pakistan

Correspondence: [*] Corresponding author. Imran Ahmed, Department of Mathematics, COMSATS University Islamabad - Lahore Campus, Lahore, Pakistan. E-mail: [email protected].

Abstract:  Let G be a finite simple graph. The line graph L (G) represents adjacencies between edges of G. We define first line simplicial complex ΔL (G) of G containing Gallai and anti-Gallai simplicial complexes ΔΓ (G) and ΔΓ′ (G) (respectively) as spanning subcomplexes. We establish the relation between Euler characteristics of line and Gallai simplicial complexes. We prove that the shellability of a line simplicial complex does not hold in general. We give formula for Euler characteristic of line simplicial complex associated to Jahangir graph Jm,n by presenting an algorithm.

Keywords: Euler characteristic, Betti number, facet ideal, connected simplicial complex, shellability

DOI: 10.3233/JIFS-190369

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 35-42, 2020