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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 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.

Keywords

Euler characteristic Betti number facet ideal connected simplicial complex shellability

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Computational aspects of line simplicial complexes

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