A Textbook of Graph Theory

by: R. Balakrishnan • K. Ranganathan

This Second Edition is a revised and enlarged edition with two new chapters—
one on domination in graphs (Chap. 10) and another on spectral properties of
graphs (Chap. 11)—and an enlarged chapter on graph coloring (Chap. 7). Chapter 10
presents the basic properties of the domination number of a graph and also deals
with Vizing’s conjecture on the domination number of the Cartesian product of
two graphs. Chapter 11 contains several results on the eigenvalues of graphs and
includes a section on the Ramanujan graphs and another on the energy of graphs.
The new additions in Chap. 7 include the introduction of b-coloring in graphs and
an extension of the discussion of the Myceilskian of a graph over what was given
in the First Edition. The sections of Chap. 10 of the First Edition that contained
some applications of graph theory have been shifted in the Second Edition to the
relevant chapters: “The Connector Problems” to Chap. 4, “The Timetable Problem”
to Chap. 5 and the “Application to Social Psychology” to Chap. 1.