# Non-contractible non-edges in 2-connected graphs

Das, Anita and Francis, Mathew C and Mathew, Rogers and Sadagopan, N (2010) Non-contractible non-edges in 2-connected graphs. In: Information Processing Letters, 110 (23). pp. 1044-1048.

 PDF Non.pdf - Published Version Restricted to Registered users only Download (163kB) | Request a copy
Official URL: http://dx.doi.org/10.1016/j.ipl.2010.09.005

## Abstract

Any pair of non-adjacent vertices forms a non-edge in a graph. Contraction of a non-edge merges two non-adjacent vertices into a single vertex such that the edges incident on the non-adjacent vertices are now incident on the merged vertex. In this paper, we consider simple connected graphs, hence parallel edges are removed after contraction. The minimum number of nodes whose removal disconnects the graph is the connectivity of the graph. We say a graph is k-connected, if its connectivity is k. A non-edge in a k-connected graph is contractible if its contraction does not result in a graph of lower connectivity. Otherwise the non-edge is non-contractible. We focus our study on non-contractible non-edges in 2-connected graphs. We show that cycles are the only 2-connected graphs in which every non-edge is non-contractible. (C) 2010 Elsevier B.V. All rights reserved.

Item Type: Journal Article Information Processing Letters Elsevier Science B.V. Copyright of this article belongs to Elsevier Science B.V. Combinatorial problems; Contraction; Contractible edges/non-edges; Connectivity Division of Electrical Sciences > Computer Science & Automation 13 Dec 2010 09:55 13 Dec 2010 09:55 http://eprints.iisc.ac.in/id/eprint/34456