Computational aspects of line simplicial complexes

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Computational aspects of line simplicial complexes

Ahmed, Imran; Muhmood, Shahid

Journal of intelligent & fuzzy systems, 01/2020, Volume: 39, Issue: 1

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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.

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