On the Laplacian coefficients and Laplacian-like energy of bicyclic graphs

Autor:	Shang-Wang Tan
Rok vydání:	2012
Předmět:	Combinatorics Discrete mathematics Indifference graph Algebra and Number Theory Resistance distance Chordal graph Cograph Maximal independent set Laplacian matrix 1-planar graph Pancyclic graph Mathematics
Zdroj:	Linear and Multilinear Algebra. 60:1071-1092
ISSN:	1563-5139 0308-1087
DOI:	10.1080/03081087.2011.643473
Popis:	Let be the characteristic polynomial of Laplacian matrix of an n-vertex graph G. We present three transforms on graphs that decrease all Laplacian coefficients c k (G), then we characterize the graphs with the minimal Laplacian-like energy, which is the sum of square roots of all roots on φ(G, λ), in the set of all bicyclic graphs with fixed order and matching number. Furthermore, we determine the graphs with the smallest and the second smallest Laplacian-like energy among all n-vertex connected bicyclic graphs except B n , where B n is the graph obtained from a four-vertex cycle C 4 by adding an edge joining two non-adjacent vertices and adding n − 4 pendant edges to a vertex of degree 3.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5c19f1556434ffcbf77e0a7b77be6f6e https://doi.org/10.1080/03081087.2011.643473 Zobrazit plný text záznamu