✦ LIBER ✦

Region distributions of some small diameter graphs

✍ Scribed by Saul Stahl

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 954 KB
Volume: 89
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90121-h

No coin nor oath required. For personal study only.

✦ Synopsis

Stahl, S., Region distributions of some small diameter graphs, Discrete Mathematics 89 (1991) 281-299. Let G be a graph with a vertex u such that V(G) -{u} induces either a forest or a cycle. It is shown that the region distribution of G is approximately proportional to the Stirling numbers of the first kind.

📜 SIMILAR VOLUMES

Nonexistence of certain cubic graphs wit

Nonexistence of certain cubic graphs with small diameters

✍ Leif K. Jørgensen 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 560 KB

We consider the maximum number of vertices in a cubic graph with small diameter. We show that a cubic graph of diameter 4 has at most 40 vertices. (The Moore bound is 46 and graphs with 38 vertices are known.) We also consider bipartite cubic graphs of diameter 5, for which the Moore bound is 62. We

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

An asymptotic formula for the number of

An asymptotic formula for the number of graphs having small diameter

✍ Ioan Tomescu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 351 KB

In this paper it is shown that for every fixed k 1> 3, G(n; d = k) = 2(~) (6.2 -k + o(1))", where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k>~2, lim,~G(n;d=k)/G(n;d=k+ 1)=lim.o~G(n;d=n-k)/ G(n;d=n-k+ 1)= oo hold.

Cubic graphs whose average number of reg

Cubic graphs whose average number of regions is small

✍ Clay Mauk; Saul Stahl 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 236 KB

Some previously investigated infinite families of cubic graphs have the property that the average number of regions of a randomly selected orientable embedding is proportional to the number of their vertices. This paper demonstrates that this property is not true of connected graphs in general. That

Characterization of the Folded Johnson G

Characterization of the Folded Johnson Graphs of Small Diameter by their Intersection Arrays

✍ Klaus Metsch 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 221 KB

It is known that the folded Johnson graphs J (2m, m) with m ≥ 16 are uniquely determined as distance regular graphs by their intersection array. We show that the same holds for m ≥ 6.

Distribution of mitochondria along small

Distribution of mitochondria along small-diameter myelinated central nervous system axons

✍ Julia M. Edgar; Mailis C. McCulloch; Christine E. Thomson; Ian R. Griffiths 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 542 KB

## Abstract Small‐diameter myelinated CNS axons are preferentially affected in multiple sclerosis (MS) and in the hereditary spastic paraplegias (HSP), in which the distal axon degenerates. Mitochondrial dysfunction has been implicated in the pathogenesis of these and other disorders involving axon