On the Laplacian Coefficients of Tricyclic Graphs with Prescribed Matching Number

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 -