# On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

Jing Luo; Zhongxun Zhu; Runze Wan

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 505-522
- ISSN: 2083-5892

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topJing Luo, Zhongxun Zhu, and Runze Wan. "On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number." Discussiones Mathematicae Graph Theory 37.3 (2017): 505-522. <http://eudml.org/doc/288503>.

@article{JingLuo2017,

abstract = {Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k $\phi (L(G)) = \det (xI - L(G)) = \sum \nolimits _\{k = 0\}^n \{( - 1)^k c_k (G)x^\{n - k\} \} $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in n,n+2(i).},

author = {Jing Luo, Zhongxun Zhu, Runze Wan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Laplacian characteristic polynomial; Laplacian-like energy; tricyclic graph},

language = {eng},

number = {3},

pages = {505-522},

title = {On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number},

url = {http://eudml.org/doc/288503},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Jing Luo

AU - Zhongxun Zhu

AU - Runze Wan

TI - On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 505

EP - 522

AB - Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k $\phi (L(G)) = \det (xI - L(G)) = \sum \nolimits _{k = 0}^n {( - 1)^k c_k (G)x^{n - k} } $ be the Laplacian characteristic polynomial of G. In this paper, we characterize the minimal graphs with the minimum Laplacian coefficients in n,n+2(i) (the set of all tricyclic graphs with fixed order n and matching number i). Furthermore, the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on ϕ(L(G)), is also determined in n,n+2(i).

LA - eng

KW - Laplacian characteristic polynomial; Laplacian-like energy; tricyclic graph

UR - http://eudml.org/doc/288503

ER -

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