id: 06054497
dt: b
an: 2014a.00768
au: Balakrishnan, R.; Ranganathan, K.
ti: A textbook of graph theory. 2nd ed.
so: Universitext. New York, NY: Springer (ISBN 978-1-4614-4528-9/pbk;
978-1-4614-4529-6/ebook). xi, 292~p. (2012).
py: 2012
pu: New York, NY: Springer
la: EN
cc: K35
ut: directed graphs; connectivity; trees; independent sets; matchings; Eulerian
graphs; Hamiltonian graphs; colorings; planar graphs; triangulated
graphs; domination in graphs; spectral properties of graphs
ci: Zbl 0938.05001
li: doi:10.1007/978-1-4614-4529-6
ab: 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.
rv: J. W. Moon (Edmonton)