Open AccessCharacteristic, admittance and matching polynomials of an antiregular graph
Author(s) -
Emanuele Munarini
Publication year - 2009
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm0901157m
Subject(s) - mathematics , interlacing , tutte polynomial , integral graph , combinatorics , laplacian matrix , eigenvalues and eigenvectors , alternating polynomial , graph , chromatic polynomial , discrete mathematics , spectral graph theory , matrix polynomial , voltage graph , polynomial , line graph , mathematical analysis , physics , quantum mechanics , computer science , operating system
An antiregular graph is a simple graph with the maximum number of vertices with different degrees. In this paper we study the characteristic polynomial, the admittance (or Laplacian) polynomial and the matching polynomial of a connected antiregular graph. For these polynomials we obtain recurrences and explicit formulas. We also obtain some spectral properties. In particular, we prove an interlacing property for the eigenvalues and we give some bounds for the energy