Algebraic Characterization of SSC of Uni-Cyclic Multigraphs  

作　　者：Imran Ahmed Shahid Muhmood 

机构地区：[1]Department of Mathematics,COMSATS University Islamabad Lahore Campus,Lahore,Pakistan

出　　处：《Algebra Colloquium》2023年第2期325-338,共14页代数集刊（英文版）

摘　　要：We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs U_(n)^(r),m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[△s(U_(n)^(r),m)]for the SSC △s(U_(n)^(r),m)(un,m).Moreover,we find the associated primes of the facet ideal I_(F)(△s(U_(n)^(r),m).Finally,we device a formula for homology groups of △s(U_(n)^(r),m) prove that the SsC of a family of uni-cyclic multigraphs is Cohen-Macaulay.

关 键 词：simplicial complexes spanning trees Hilbert series vertex covers Betti numbers 

分 类 号：O153[理学—数学]