567 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
Arithmetic completely regular codes
In this paper, we explore completely regular codes in the Hamming graphs and
related graphs. Experimental evidence suggests that many completely regular
codes have the property that the eigenvalues of the code are in arithmetic
progression. In order to better understand these "arithmetic completely regular
codes", we focus on cartesian products of completely regular codes and products
of their corresponding coset graphs in the additive case. Employing earlier
results, we are then able to prove a theorem which nearly classifies these
codes in the case where the graph admits a completely regular partition into
such codes (e.g, the cosets of some additive completely regular code).
Connections to the theory of distance-regular graphs are explored and several
open questions are posed.Comment: 26 pages, 1 figur
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
Effective metadata for social book search from a user perspective
Abstract. In this extended abstract we describe our participation in the INEX 2014 Interactive Social Book Search Track. In previous work, we have looked at the impact of professional and user-generated metadata in the context of book search, and compared these different categories of metadata in terms of retrieval effectiveness. Here, we take a different approach and study the use of professional and user-generated metadata of books in an interactive setting, and the effectivity of this metadata from a user perspective. We compare the perceived usefulness of general descriptions, publication metadata, user reviews and tags in focused and open-ended search tasks, based on data gathered in the INEX Interactive Social Book Search Track. Furthermore, we take a tentative look at the actual use of different types of metadata over time in the aggregated search tasks. Our preliminary findings in the surveyed tasks indicate that user reviews are generally perceived to be more useful than other types of metadata, and they are frequently mentioned in users ’ rationales for selecting books. Furthermore, we observe a varying usage frequency of traditional and user-generated metadata across time in the aggregated search tasks, pro-viding initial indications that these types of metadata might be useful at different stages of a search task.
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