Computational aspects of line simplicial complexes
Imran Ahmed, Shahid Muhmood · Journal of Intelligent & Fuzzy Systems · 2020
Let G be a finite simple graph. The line graph L ( G ) represents adjacencies between edges of G . We define first line simplicial complex Δ L ( G ) of G containing Gallai and anti-Gallai simplicial complexes Δ Γ ( G ) and Δ Γ ′ ( 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 J m , n by presenting an algorithm.