Computational aspects of line simplicial complexes

摘要

LetGbe a finite simple graph. The line graph L(G) represents adjacencies between edges ofG. We define first line simplicial complex Delta(L) (G) of G containing Gallai and anti-Gallai simplicial complexes Delta(Gamma)(G) and Delta(Gamma')(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.