✦ LIBER ✦

Connectivity and diameter in distance graphs

✍ Scribed by Lucia Draque Penso; Dieter Rautenbach; Jayme Luiz Szwarcfiter

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 111 KB
Volume: 57
Category: Article
ISSN: 0028-3045
DOI: 10.1002/net.20397

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Distance connectivity in graphs and digr

Distance connectivity in graphs and digraphs

✍ Balbuena, M. C.; Carmona, A.; Fiol, M. A. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 642 KB

Let G = ( V , A ) be a digraph with diameter D # 1. For a given integer 2 5 t 5 D , the t-distance connectivity K ( t ) of G is the minimum cardinality of an z --+ y separating set over all the pairs of vertices z, y which are a t distance d(z, y) 2 t. The t-distance edge connectivity X ( t ) of G i

Antipodal distance-regular graphs of dia

Antipodal distance-regular graphs of diameter four and five

✍ Tilla Schade 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 179 KB 👁 2 views

An antipodal distance-regular graph of diameter four or five is a covering graph of a connected strongly regular graph. We give existence conditions for these graphs and show for some types of strongly regular graphs that no nontrivial covers exist.

On the connectivity and the conditional

On the connectivity and the conditional diameter of graphs and digraphs

✍ Balbuena, C.; Carmona, A.; F�brega, J.; Fiol, M. A. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 771 KB

Recently, it was proved that if the diameter D of a graph G is small enough in comparison with its girth, then G is maximally connected and that a similar result also holds for digraphs. More precisely, if the diameter D of a digraph G satisfies D 5 21 -1, then G has maximum connectivity ( K = 6 ) .

On the fault-tolerant diameter and wide

On the fault-tolerant diameter and wide diameter of ω-connected graphs

✍ Jian-Hua Yin; Jiong-Sheng Li; Guo-Liang Chen; Cheng Zhong 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 179 KB

Valency of Distance-regular Antipodal Gr

Valency of Distance-regular Antipodal Graphs with Diameter 4

✍ Štefko Miklavič 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 141 KB

Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for

Nonexistence of some Antipodal Distance-

Nonexistence of some Antipodal Distance-regular Graphs of Diameter Four

✍ Aleksandar Jurišić; Jack Koolen 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 160 KB

We find an inequality involving the eigenvalues of a regular graph; equality holds if and only if the graph is strongly regular. We apply this inequality to the first subconstituents of a distance-regular graph and obtain a simple proof of the fundamental bound for distance-regular graphs, discovere