✦ LIBER ✦

Proof of a conjecture in domination theory

✍ Scribed by Igor E. Zverovich

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 76 KB
Volume: 184
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(93)e0231-r

No coin nor oath required. For personal study only.

✦ Synopsis

A dominating set D of a graph G is a least dominating set (I.d.s) if y((D)) < 2~((D~)) for any dominating set D1 (7 denotes domination number). The least domination number ~ ~ (G) of G is the minimum cardinality of a 1.d.s. We prove a conjecture of Sampathkumar (1990) that Vl ~< 3p/5 for any connected graph G of order p/> 2.

📜 SIMILAR VOLUMES

Proof of a conjecture on game domination

✍ O. Favaron; H. Karami; R. Khoeilar; S. M. Sheikholeslami; L. Volkmann 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 87 KB 👁 1 views

## Abstract The game domination number of a (simple, undirected) graph is defined by the following game. Two players, \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${\mathcal{A}}$\end{document} and \docume

Proof of a conjecture on -tuple dominati

Proof of a conjecture on -tuple domination in graphs

✍ Guangjun Xu; Liying Kang; Erfang Shan; Hong Yan 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 142 KB

Let G = (V, E) be a graph and N G [v] the closed neighborhood of a vertex v in G. For k ∈ N, the minimum cardinality of a set In this note we prove the following conjecture of Rautenbach and Volkmann [D. Rautenbach, L. Volkmann, New bounds on the k-domination number and the k-tuple domination numbe

The Proof of a Conjecture of Additive Nu

The Proof of a Conjecture of Additive Number Theory

✍ Alexandru Gica 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 94 KB

The aim of this paper is to show that for any n ¥ N, n > 3, there exist a, b ¥ N\* such that n=a+b, the ''lengths'' of a and b having the same parity (see the text for the definition of the ''length'' of a natural number). Also we will show that for any n ¥ N, n > 2, n ] 5, 10, there exist a, b ¥ N\

A proof of Boesch's conjecture

✍ Guifang Wang 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 596 KB

Proof of a conjecture of nirenberg

✍ Robert Osserman 📂 Article 📅 1959 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB 👁 1 views

Proof of a Chromatic Polynomial Conjectu

Proof of a Chromatic Polynomial Conjecture

✍ F.M. Dong 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 138 KB

Let P(G, \*) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number \* n, (\*&2) n&1 P(G, \*)&\*(\*&1) n&2 P(G, \*&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1))