A Note on the Matching Polynomials of Paths and Cycles

ZHANG Hai-liang

doi:10.13371/j.cnki.chin.q.j.m.2018.02.004

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 2: 140 - 143

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.02.004

A Note on the Matching Polynomials of Paths and Cycles

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Department of Mathematics, Taizhou University

ZHANG Hai-liang(1976-), LeDu Qinghai China. Associated Professor of TaiZhou University, Research Fields: Graph theory and its applications.

Accepted date: 2016-10-15

Online published: 2020-10-09

Supported by

Supported by the Natural Science Foundation of the People’s Republic of China under Grant(11571252)；

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Abstract

The spectra of matching polynomials which are useful in the computations of resonance energy and grand canonical partition functions of molecular’s. It also present other properties for certain classes of graphs and lattices. In [1] Balasubramanian calculates several matching polynomials and matching roots of several molecular graphs. He found that the matching polynomial of C₆, C₁₀, C₁₄, C₁₈ and C₂₂ are divided by x²-2. In this note,we prove that x²-2 divides MC_4k+2（x）, k = 1, 2,..., n and obtain some other properties of matching polynomials of paths and cycles.

Key words： Graph algorithms; Matching polynomial; Matching roots; Combinatorial problems

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ZHANG Hai-liang . A Note on the Matching Polynomials of Paths and Cycles[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(2) : 140 -143 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.02.004

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