首页|Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs
Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs
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Research on the independence polynomial of graphs has been very active.However,the computational complexity of determining independence polynomials for general graphs remains NP-hard.Let α(G)be the independence number of G and i(G;k)be the number of independent sets of order k in G,then the independence polynomial is defined as I(G;x)=α(G)∑k=0i(G;k)xk,i(G;0)=1.In this paper,by utilizing the transfer matrix,we obtain an analytical expression for I(CGn;x)of mono-cylindrical grid graphs CGn and present a crucial proof of it.Moreover,we also explore the Merrifield-Simmons index and other properties of CGn.
Independence polynomialCylindrical grid graphsTransfer matrixMerrifield-Simmons index
JI Lin-xing、ZHANG Ke、HU Wen-jun
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School of Information Engineering,Huzhou University,Huzhou 313000,China
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