A textbook of graph theory
type: Item
instance of: scholarly article
title: A textbook of graph theory
zbMATH Open document ID: 1254.05001
DOI: 10.1007/978-1-4614-4529-6
published in: Universitext
publication date: 2012-07-11T00:00:00Z
review text: The first edition of this text was reviewed in [Zbl 0938.05001]. The chapter on graph colorings has been expanded with material on b-colorings and homomorphisms, among other things. There are also new chapters devoted to two areas of considerable research activity in recent years. One of these presents a number of relations involving domination-type parameters; and, in particular, contains the Barkalkin-German proof that Vizing's conjecture on the domination number of the Cartesian product of two graphs holds for decomposable graphs. The other presents results on spectral properties of various graphs, including a proof of Sachs's theorem on the spectrum of the line graph of a regular graph. A parameter borrowed from chemistry, the energy of a graph, is also defined and results on this parameter are obtained for certain graphs. The list of references now contains 195 items.
Mathematics Subject Classification ID: 05-01
Mathematics Subject Classification ID: 05Cxx
zbMATH DE Number: 6054497
zbMATH Keywords: directed graphs
zbMATH Keywords: connectivity
zbMATH Keywords: trees
zbMATH Keywords: independent sets
zbMATH Keywords: matchings
zbMATH Keywords: Eulerian graphs
zbMATH Keywords: Hamiltonian graphs
zbMATH Keywords: colorings
zbMATH Keywords: planar graphs
zbMATH Keywords: triangulated graphs
zbMATH Keywords: domination in graphs
zbMATH Keywords: spectral properties of graphs
reviewed by: J. W. Moon
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4614-4529-6
OpenAlex ID: W4244148219
author: R. Balakrishnan
author: K. Ranganathan
description: scientific article; zbMATH DE number 6054497