On acyclic systems with minimal Hosoya index. (English) Zbl 0999.05020
Summary: The Hosoya index of a graph is defined as the total number of independent edge subsets of the graph. We characterize the trees with a given size of matching and having minimal and second minimal Hosoya index.
MSC:
| 05C05 | Trees |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C75 | Structural characterization of families of graphs |
| 05C35 | Extremal problems in graph theory |
References:
| [1] | Chan, O.; Gutman, I.; Lam, T. K.; Merris, R., Algebraic connections between topological indices, J. Chem. Inform Comput. Sci., 38, 62-65 (1998) |
| [2] | Gutman, I., Acyclic systems with extremal Hückel \(π\)-electron energy, Theor. Chim. Acta, 45, 79-87 (1977) |
| [3] | Gutman, I., Acyclic conjugated molecules, trees and their energies, J. Math. Chem., 29, 123-143 (1987) |
| [4] | Gutman, I.; Polansky, O. E., Mathematical Concepts in Organic Chemistry (1986), Springer: Springer Berlin · Zbl 0657.92024 |
| [5] | Hosoya, H., Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn., 44, 2332-2339 (1971) |
| [6] | Li, H., On minimal energy ordering of acyclic conjugated molecules, J. Math. Chem., 25, 145-169 (1999) · Zbl 1002.92570 |
| [7] | Minc, H., Permanents (1978), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0401.15005 |
| [8] | Zhang, F.; Li, H., On acyclic conjugated molecules with minimal energies, Discrete Appl. Math., 92, 71-84 (1999) · Zbl 0920.92037 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
