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Title: Inequalities of Nordhausgaddum type for doubly connected domination
Authors: Roslan, Hasni@Abdullah
S.M., Sheikholeslami
M. Hadi, Akhbari
???metadata.dc.contributor.url???: hroslan@cs.usm.my
s.m.sheikholeslame@azaruniv.edu
hadiakhbari@gmail.com
Keywords: Regional Conference on Applied and Engineering Mathematics (RCAEM);Nordhaus;Gaddum
Issue Date: 2-Jun-2010
Publisher: Universiti Malaysia Perlis (UniMAP)
???metadata.dc.publisher.department???: Institut Matematik Kejuruteraan
Citation: p.1
Series/Report no.: Proceedings of the 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010
Abstract: Many problems in extremal graph theory seek the extreme values of graph parameters on families of graphs. Results of Nordhaus-Gaddum type study the extreme values of the sum (or product) of a parameter on a graph and its complement, following the classic paper of Nordhaus and Gaddum solving these problems for the chromatic number on n- vertex graphs. In this paper, we study such problems for the doubly connected domination number. A set S of vertices of a connected graph G is a doubly connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraphs induced by S and V - S are connected. The doubly connected domination number cc(G) is the minimum size of such a set. We prove that when G and G are both connected of order n, cc(G) + cc(G) n + 2 and we describe the two in nite families of extremal graphs achieving the bound.
Description: 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.
URI: http://hdl.handle.net/123456789/10252
Appears in Collections:Conference Papers

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