For a given non-adjacent pair {x, y} in a graph G, we denote by Gxy the graph obtained by deleting x and y and adding a new vertex xy adjacent to precisely those vertices of G-x-y which were adjacent to at least one of x or y in G. We say that Gxy is obtained by contracting on {x, y}. In this paper we introduce -stable graphs and we have established that γstable trees have a unique structure. © 2013 Academic Publications, Ltd.

Yamuna M

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Karthika K

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

&nbsp;

&nbsp;

VIT University

International Journal of Pure and Apllied Mathematics

Planar graph characterization is always of interest due to its complexity in characterization. In this paper, we obtain a necessary and sufficient condition for a graph to be NDSS and hence characterize the planarity and outer - planarity of its complement G. © Published under licence by IOP Publishing Ltd.

Fulltext

IOP Conference Series: Materials Science and Engineering

Planar graph characterization of NDSS graphs

Subdividing an edge in the graph may increase the domination number or remains the same. In this paper, we introduce a new kind of graph called non - domination subdivision stable graph (NDSS). We obtain a necessary and sufficient condition for a graph to be NDSS. We provide a constructive characterization of NDSS trees and a MATLAB program for identifying NDSS graphs. © Published under licence by IOP Publishing Ltd.

Non - domination subdivision stable graphs

Let G1 and G2 be two undirected graphs, (v w) be an edge of G1, and (x y) be an edge of G2. Hajos construction forms a new graph H, that combines the two graphs by identifying vertices v and x into a single vertex, removing the two edges (v w) and (x y), and adding a new edge (w y). In this paper we introduce a new kind of graph called the Hajos stable graph, where the stable property is defined using the domination number of graphs G1 and G2. We have obtained a necessary and sufficient condition for graphs G1 and G2 to be Hajos stable.

Journal	International Journal of Pure and Apllied Mathematics
Publisher	Academic Publications
ISSN	1311-8080
Open Access	No