✦ LIBER ✦

Voltage graph embeddings and the associated block designs

✍ Scribed by Brian L. Garman

Publisher: John Wiley and Sons
Year: 1979
Tongue: English
Weight: 663 KB
Volume: 3
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190030107

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The voltage graph construction of Gross (orientable case) and Stahl as well as Gross and Tucker (nonorientable case) is extended to the case where the base graph is embedded in a pseudosurface or a generalized pseudosurface. This theory is then applied to produce triangular embeddings of K~4(n)~; they in turn yield an infinite class of partially balanced incomplete block designs.

📜 SIMILAR VOLUMES

Zero-sum block designs and graph labelin

Zero-sum block designs and graph labelings

✍ Zsolt Tuza 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 621 KB

Proving a conjecture of Aigner and Triesch, we show that every graph G = (V,E) without isolated vertices and isolated edges admits an edge labeling 5: E -{0,1}" with binary vectors of length m = [log2 nl + 1 such that the sums 6 ( v ) := 1 ; ; ; &(e) (taken modulo 2 componentwise) are mutually disti

Cycles in the block-intersection graph o

Cycles in the block-intersection graph of pairwise balanced designs

✍ Donovan R. Hare 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 580 KB

It is shown that the block-intersection graph of a pairwise balance design with ),= l is edge-pancyclic given that its minimum block cardinality is at least 3.

Existential closure of block intersectio

Existential closure of block intersection graphs of infinite designs having finite block size and index

✍ David A. Pike; Asiyeh Sanaei 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 129 KB

In this article we study the n-existential closure property of the block intersection graphs of infinite t-(v, k, k) designs for which the block size k and the index k are both finite. We show that such block intersection graphs are 2-e.c. when 2 ≤ t ≤ k-1. When k = 1 and 2 ≤ t ≤ k, then a necessary

General Analysis of Covariance Models fo

General Analysis of Covariance Models for the Split Block and Related Block Designs

✍ C. J. Monlezun; D. C. Blouin 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 637 KB

Exact test statiatica and confidence intervals for a general Split block ANOCOVA model are derived. With a single covariete, each Statistic for testing main effect A, main effect B, and the A X B interaction has one less numerator degree of freedom than ita counterpart in the ordinary ANOVA without

On the E-Optimality of Block Designs wit

On the E-Optimality of Block Designs with Unequal Block Sizes

✍ Dr. Henryk Brzeskwiniewicz 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 192 KB 👁 2 views

In this paper an inequality for the smallest positive eigenvalues of the \_C-matrix of a block design are derived. This inequality is a generalization of a result by CONSTANTINE (1982) to the caw of unequal block sizes. On the basis of the above result a certain E-optimality criterium of block desig

Blocks and the nonorientable genus of gr

Blocks and the nonorientable genus of graphs

✍ Saul Stahl; Lowell W. Beineke 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB 👁 1 views

## Abstract Examples are given to show that the nonorientable genus of a graph is not additive over its blocks. A nonorientable analog for the Battle, Harary, Kodama, and Youngs Theorem is proved; this completely determines the nonorientable genus of a graph in terms of its blocks. It is also shown