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Abstract

Let Δ_Γ (G) be Gallai simplicial complex defined as a generalization of Gallai graph Γ (G) such that G is a finite simple graph. The Betti numbers are topological objects which were proved to be invariants by Poincaré. In this note, we give formula for Betti numbers of Gallai simplicial complex associated to prism graph by coding in MATLAB. We prove that a simple graph G having n vertices of the form n = 3l + 2 or 3l + 3 is f-Gallai graph for $G = 𝕊_{4 l}$ (respectively $G = 𝕊_{4 l + 1}$ ) a graph consisting of star graphs S_2l and $S_{2 l}^{'}$ (respectively S_2l and S_2l+1) with l common vertices such that l ≥ 2.

Keywords

Betti number Gallai simplicial complex

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Gallai simplicial complexes

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