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| Title: | Inequalities of Nordhausgaddum type for doubly connected domination |
| Authors: | Roslan, Hasni@Abdullah
S.M., Sheikholeslami
M. Hadi, Akhbari |
| E-mail: | 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) |
| 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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Files in This Item:
| File |
Description |
Size | Format |
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| R047.pdf | Access is limited to UniMAP community | 56.11 kB | Adobe PDF | View/Open |
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