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Extremal phenylene chains with respect to the coefficients sum of the permanental polynomial, the spectral radius, the Hosoya index and the Merrifield-Simmons index. (English) Zbl 1428.05156

Summary: In this paper, the extremal problems on the phenylene chains with respect to some graph invariants are studied. All the graphs minimizing (resp. maximizing) the coefficients sum of the permanental polynomial, the spectral radius, the Hosoya index and the Merrifield-Simmons index among all the phenylene chains each of which contains \(n\) four-membered rings are identified.

MSC:

05C35 Extremal problems in graph theory
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C31 Graph polynomials
05C90 Applications of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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