On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

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

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Abstract

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Let [...] φ(L(G))=det (xI−L(G))=∑k=0n(−1)kck(G)xn−k $\phi \left(L\left(G\right)\right)=det\left(xI-L\left(G\right)\right)={\sum }_{k=0}^{n}{\left(-1\right)}^{k}{c}_{k}\left(G\right){x}^{n-k}$ 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).

How to cite

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Jing 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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