✦ LIBER ✦

On the product of upper irredundance numbers of a graph and its complement

✍ Scribed by E.J. Cockayne; C.M. Mynhardt

Publisher: Elsevier Science
Year: 1989
Tongue: English
Weight: 471 KB
Volume: 76
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90304-x

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

The product of the independent dominatio

The product of the independent domination numbers of a graph and its complement

✍ E.J. Cockayne; O. Favaron; H. Li; G. MacGillivray 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 240 KB

The sequence of upper and lower dominati

The sequence of upper and lower domination, independence and irredundance numbers of a graph

✍ E.J. Cockayne; C.M. Mynhardt 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 803 KB

Necessary and sufficient conditions are established for the existence of a graph whose upper and lower domination, independence and irredundance numbers are six given positive integers. This result shows that the only relationships between these six parameters which hold for all graphs and which do

The irredundance number and maximum degr

The irredundance number and maximum degree of a graph

✍ B. Bollobás; E.J. Cockayne 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 104 KB

A vertex x in a subset X of vertices of an undirected graph is redundant if its dosed neighborhood is contained in the union of closed neighborhoods of vertices of X-{x}. In the context of a communications network, this means that any vertex that may receive communications from X may also be irdorme

The minimum number of subgraphs in a gra

The minimum number of subgraphs in a graph and its complement

✍ Lane Clark 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 265 KB 👁 2 views

## Abstract For a graphb __F__ without isolated vertices, let __M__(__F__; __n__) denote the minimum number of monochromatic copies of __F__ in any 2‐coloring of the edges of __K__~__n__~. Burr and Rosta conjectured that when __F__ has order __t__, size __u__, and __a__ automorphisms. Independent

Some upper bounds for the product of the

Some upper bounds for the product of the domination number and the chromatic number of a graph

✍ Jerzy Topp; Lutz Volkmann 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 199 KB

Topp, J. and L. Volkmann, Some upper bounds for the product of the domination number and the chromatic number of a graph, Discrete Mathematics 118 (1993) 2899292. Some new upper bounds for yx are proved, where y is the domination number and x is the chromatic number of a graph. All graphs consider

The ratio of the irredundance number and

The ratio of the irredundance number and the domination number for block-cactus graphs

✍ Zverovich, V. E. 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB 👁 2 views

Let γ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43-56] and Bollobás and Cock- ayne [J. Graph Theory (1979) 241-249] proved independently that γ(G) < 2ir(G) for