SPANNING SIMPLICIAL COMPLEXES OF n-CYCLIC GRAPHS WITH A COMMON EDGE

Abstract

Abstract. In this paper, we characterize some algebraic and combinatorial properties of spanning simplicial complex ∆s(Gt 1 , t 2 , ··· , tn ) of the class of the n-cyclic graphs Gt 1 , t 2 , ··· , tn with a common edge. We show that ∆s(Gt 1 , t 2 , ··· , tn ) is pure simplicial complex of dimension n i=1 t i − 2n, and we also determine the Stanley-Reisner ideal I ∆s(G t 1 , t 2 , ··· , t n ) of ∆s(Gt 1 , t 2 , ··· , tn ) and its primary decomposition. Under the condition that the length of every cyclic graph Gt i is t for 1 ≤ i ≤ n, we give a formula for f -vector of ∆s(Gt 1 , t 2 , ··· , tn ) and consequently a formula for Hilbert series of the StanleyReisner ring k[∆s(Gt 1 , t 2 , ··· , tn )], where k is a field.Mathematics Subject Classification (2010): 13P10, 13H10, 13F20, 13C14

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