The Sum and Product of Independence Numbers of Graphs and their Line Graphs

Susanth C., Sunny Joseph Kalayathankal


The bounds on the sum and product of chromatic numbers of a graph and its complement are known as Nordhaus-Gaddum inequalities. In this paper, we study the bounds on the sum and product of the independence numbers of graphs and their line graphs. We also provide a new characterization of the certain graph classes.


Independence number; Matching number; Line graph

Full Text:



A. Brandstadt, V. B. Le and J. P. Spinard, Graph Classes: A Survey, SIAM, Philadelphia, (1999).

J. A. Bondy and U. S. R. Murty, Graph Theory, Springer, (2008).

A. E. Brouwer, A. M. Cohen and A. Neumaier,Distance-Regular Graphs. New York: Springer-Verlag, 1989.

G. Chartrand, Ping Zhang, Chromatic Graph Theory, CRC Press, Western Michigan University Kalamazoo, MI, U.S.A.

J. Clark and D. A. Holton, A First Look At Graph Theory, Allied Pub., India, (1991).

K. L. Collins, Ann Trenk, Nordhaus-Gaddum theorem for the distinguishing chromatic number, The electronic journal of combinatorics 16 (2009), arXiv:1203.5765v1 [math.CO], 26 March (2012).

N. Deo, Graph Theory with Applications to Engineering and Computer Science, PHI Learning, (1974).

R. Diestel, Graph Theory, Springer-Verlag New York 1997, (2000).

J. A. Gallian, A Dynamic survey of Graph Labeling, the electronic journal of combinatorics 18, (2011).

F. Harary, Graph Theory, Addison-Wesley Publishing Company Inc, (1994).

D. B. West, Introduction to Graph Theory, Pearson Education Asia, (2002).

R. J. Wilson, Introduction to Graph Theory, Prentice Hall, (1998).

Information System on Graph Classes and their Inclusions,


eISSN 0975-5748; pISSN 0974-875X