1,103 research outputs found
On Distance-Regular Graphs with Smallest Eigenvalue at Least
A non-complete geometric distance-regular graph is the point graph of a
partial geometry in which the set of lines is a set of Delsarte cliques. In
this paper, we prove that for fixed integer , there are only finitely
many non-geometric distance-regular graphs with smallest eigenvalue at least
, diameter at least three and intersection number
Another construction of edge-regular graphs with regular cliques
We exhibit a new construction of edge-regular graphs with regular cliques
that are not strongly regular. The infinite family of graphs resulting from
this construction includes an edge-regular graph with parameters . We
also show that edge-regular graphs with -regular cliques that are not
strongly regular must have at least vertices.Comment: 7 page
Equiangular lines in Euclidean spaces
We obtain several new results contributing to the theory of real equiangular
line systems. Among other things, we present a new general lower bound on the
maximum number of equiangular lines in d dimensional Euclidean space; we
describe the two-graphs on 12 vertices; and we investigate Seidel matrices with
exactly three distinct eigenvalues. As a result, we improve on two
long-standing upper bounds regarding the maximum number of equiangular lines in
dimensions d=14, and d=16. Additionally, we prove the nonexistence of certain
regular graphs with four eigenvalues, and correct some tables from the
literature.Comment: 24 pages, to appear in JCTA. Corrected an entry in Table
Characterizing Block Graphs in Terms of their Vertex-Induced Partitions
Given a finite connected simple graph with vertex set and edge
set , we will show that
the (necessarily unique) smallest block graph with vertex set whose
edge set contains is uniquely determined by the -indexed family of the various partitions
of the set into the set of connected components of the
graph ,
the edge set of this block graph coincides with set of all -subsets
of for which and are, for all , contained
in the same connected component of ,
and an arbitrary -indexed family of
partitions of the set is of the form for some
connected simple graph with vertex set as above if and only if,
for any two distinct elements , the union of the set in
that contains and the set in that contains coincides with
the set , and holds for all .
As well as being of inherent interest to the theory of block graphs, these
facts are also useful in the analysis of compatible decompositions and block
realizations of finite metric spaces
Modelling information routing with noninterference
To achieve the highest levels of assurance, MILS architectures need to be formally analysed. A key challenge is to reason about the interaction between the software applications running on top of MILS core components, such as the separation kernel. In this paper, we extend Rushby's model of noninterference with explicit information units and domain programs. These extensions enable the reasoning at an abstract level about systems built on top of noninterference. As an illustration of our approach, we formally model and analyse an example inspired by the GWV Firewall. <br/
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