Perfect Octagon Quadrangle Systems with an upper C4-system and a large spectrum

An octagon quadrangle is the graph consisting of an 8-cycle (x1, x2,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order ν and index λ [OQS] is a pair (X,H), where X is a finite set of ν vertices and H is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKν defined on X. An octagon quadrangle system Σ=(X,H) of order ν and index λ is said to be upper C4-perfect if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν; it is said to be upper strongly perfect, if the collection of all of the upper 4-cycles contained in the octagon quadrangles form a μ-fold 4-cycle system of order ν and also the collection of all of the outside 8-cycles contained in the octagon quadrangles form a ρ-fold 8-cycle system of order ν. In this paper, the authors determine the spectrum for these systems, in the case that it is the largest possible

ON THE SPECTRUM OF OCTAGON QUADRANGLE SYSTEMS OF ANY INDEX

An \emph{octagon quadrangle} is the graph consisting of a length $8$ cycle $(x_{1},x_{2},\dots,x_{8})$ and two chords, $\{x_{1},x_{4}\}$ and $\{x_{5},x_{8}\}$. An \emph{octagon quadrangle system} of order $v$ and index $\lambda$ is a pair $(X,\mathcal B)$, where $X$ is a finite set of $v$ vertices and $\mathcal B$ is a collection of octagon quadrangles (called blocks) which partition the edge set of $\lambda K_{v}$, with $X$ as vertex set. In this paper we determine completely the spectrum of octagon quadrangle systems for any index $\lambda$, with the only possible exception of $v=20$ for $\lambda=1$

strongly balanced 4 kite designs nested into oq systems

In this paper we determine the spectrum for octagon quadrangle systems [OQS] which can be partitioned into two strongly balanced 4-kitedesigns

Distance-regular graphs

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page

Material Expressions of Class, Status and Authority amongst Commissioned Officers at Fort Yamhill and Fort Hoskins, Oregon, 1856-1866

During the 19th century the United States Army was a military institution characterized by a hierarchical system of authoritative, social and economic inequality between members of its different military grades. Although necessary for insuring military discipline within the Army this system of inequality also influenced the non-military social lives of commissioned officers and their families and colored much of military life with a non-military consumerist tint. This dissertation examines the material expression of military authority, social status and economic position amongst three grades of commissioned officers who served at two mid-19th century United States Army posts in western Oregon, Fort Yamhill and Fort Hoskins. Using historical and archaeological records associated with 47 company grade officers this dissertation demonstrates that the commissioned officers who served at these posts were highly competitive individuals who used their military rank and military salaries to express their social and economic status through the economic behaviors of conspicuous consumption and conspicuous leisure and to demonstrate their membership as socio-cultural elites within the upper classes of 19th century America