On Distance-Regular Graphs with Smallest Eigenvalue at Least −m-m

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 $m\geq 2$, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least $-m$, diameter at least three and intersection number $c_2 \geq 2$

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 $(24,8,2)$. We also show that edge-regular graphs with $1$-regular cliques that are not strongly regular must have at least $24$ 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

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.