1,720,960 research outputs found
A complete solution to the spectrum problem for graphs with six vertices and up to nine edges
Get PDFLet be a graph. A -design of order is a decomposition of the complete graph into disjoint copies of . The existence problem of graph designs has been completely solved for all graphs with up to five vertices, and all graphs with six vertices and up to seven edges; and almost completely solved for all graphs with six vertices and eight edges leaving two cases of order 32 unsettled. Up to isomorphism there are 20 graphs with six vertices and nine edges (and no isolated vertex). The spectrum problem has been solved completely for 11 of these graphs, and partially for 2 of these graphs. In this article, the two missing graph designs for the six-vertex eight-edge graphs are constructed, and a complete solution to the spectrum problem for the six-vertex nine-edge graphs is given; completing the spectrum problem for all graphs with six vertices and up to nine edges
Decomposition of Complete Graphs into Isomorphic Complete Bipartite Graphs
No full textA decomposition of a complete graph K-n into disjoint copies of a complete bipartite graph K-s,K- t is called a K-s,K- t-design of order n. The existence problem of K-s,K- t-designs has been completely solved for the graphs K-1,K- k for k >= 1, K-2a,K-2b for a, b >= 1, K-2,K-3 and K-3,K-3. In this paper, I prove that for all s, t >= 1, if there exists a K-s,K- t-design of order N, then there exists a K-s,K- t-design of order n for all n equivalent to N (mod 2st) and n >= N. Giving necessary direct constructions, I provide an almost complete solution for the existence problem for complete bipartite graphs with fewer than 18 edges, leaving five orders in total unsolved. (C) 2012 Wiley Periodicals, Inc
)‐Designs of Orders 27, 135, 162, and 216
No full textThe problem of the existence of a decomposition of the complete graph Kn into disjoint copies of K-5\e has been solved for all admissible orders n, except for 27, 36, 54, 64, 72, 81, 90, 135, 144, 162, 216, and 234. In this paper, I eliminate 4 of these 12 unresolved orders. Let Gamma be a (K-27, K-5\e)-design. I show that | Aut(Gamma)| divides 2k3 for some k = 0 and that Sym(3) not less than or equal to Aut(Gamma). I construct (K-27, K-5\e)-designs by prescribing Z6 as an automorphism group, and show that up to isomorphism there are exactly 24 (K-27, K-5\e)-designs with Z6 as an automorphism group. Moreover, I show that the full automorphism group of each of these designs is indeed Z6. Finally, the existence of (K-5\e)-designs of orders 135, 162, and 216 follows immediately by the recursive constructions given by G. Ge and A. C. H. Ling, SIAM J Discrete Math 21(4) (2007), 851-864. (C) C 2012 Wiley Periodicals, Inc
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
On Minimal Defining Sets of Full Designs and Self-Complementary Designs, and a New Algorithm for Finding Defining Sets of t-Designs
No full textA defining set of a t-(v, k, lambda) design is a partial design which is contained in a unique t- design with the given parameters. A minimal defining set is a defining set, none of whose proper partial designs is a defining set. This paper proposes a new and more efficient algorithm that finds all non-isomorphic minimal defining sets of a given t- design. The complete list of minimal defining sets of 2-(6, 3, 6) designs, 2-(7, 3, 4) designs, the full 2-(7, 3, 5) design, a 2-(10, 4, 4) design, 2-(10, 5, 4) designs, 2-(13, 3, 1) designs, 2-(15, 3, 1) designs, the 2-(25, 5, 1) design, 3-(8, 4, 2) designs, the 3-(12, 6, 2) design, and 3-(16, 8, 3) designs are given to illustrate the efficiency of the algorithm. Also, corrections to the literature are made for the minimal defining sets of four 2-(7, 3, 3) designs, two 2-(6, 3, 4) designs and the 2-(21, 5, 1) design. Moreover, an infinite class of minimal defining sets for 2-((v)(3)) designs, where v >= 5, has been constructed which helped to show that the difference between the sizes of the largest and the smallest minimal defining sets of 2-((v)(3)) designs gets arbitrarily large as v -> infinity. Some results in the literature for the smallest defining sets of t-designs have been generalized to all minimal defining sets of these designs. We have also shown that all minimal defining sets of t-(2n, n, lambda) designs can be constructed from the minimal defining sets of their restrictions when t is odd and all t-(2n, n, lambda) designs are self-complementary. This theorem can be applied to 3-(8, 4, 3) designs, 3-(8, 4, 4) designs and the full 3-((8)(4)) design using the previous results on minimal defining sets of their restrictions. Furthermore we proved that when n is even all (n - 1)-(2n, n, lambda) designs are self-complementary
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