IJPAM: Volume 101, No. 5 (2015)

$K$-EXTENDABILITY IN GRAPHS

K. Angaleeswari$^1$, P. Sumathi$^2$, V. Swaminathan$^3$
$^1$Department of Mathematics
Thiagarajar College of Engineering
Madurai 15, INDIA
$^2$Department of Mathematics
C.K.N.College for Men
Chennai, INDIA
$^3$Saraswathy Narayanan College
Madurai, 18, INDIA


Abstract. A graph G =$(V,E)$ is said to be k-extendable where k is a positive integer, if every independent set of $G$ of cardinality k is contained in a maximum independent set of $G$. 1-extendable graphs are also called $\beta_0$-excellent graphs (or) Berge graphs. A study of k-extendable graphs has been made in [9,10]. In this paper almost k-extendable graphs are studied for specific values of k. That is those graphs which are not k-extendable for exactly one value of k namely $k=1,2,(\beta_0(G)-1),(\beta_0(G)-2)$ and $(\beta_0(G)-3)$.

Received: March 12, 2015

AMS Subject Classification: 05C69

Key Words and Phrases: Berge graph, k-extendability

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DOI: 10.12732/ijpam.v101i5.22 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 5
Pages: 801 - 809


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