1,720,971 research outputs found
On Mixed Cages
Full text linkMixed graphs have both directed and undirected edges. A mixed cage is a
regular mixed graph of given girth with minimum possible order. In this paper
mixed cages are studied. Upper bounds are obtained by general construction
methods and computer searches
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Some Applications of pq-groups in Graph Theory
No full textWe describe some new applications of nonabelian pq-groups to construction problems in Graph Theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers. For primes p and q such that p < q and q ≡ 1 (mod p), there exists a nonabelian group of order pq, which is a semidirect product of Zq by Zp [3]. In this note, we use these groups to construct several graphs and graph colorings. Let G be a nonabelian pq-group and let a and b be elements of orders p and q, respectively. The subgroup generated by b is normal in G and a −1 ba = b r where r p ≡ 1 (mod q). So the elements of G can be represented in the form a i b j, for 0 ≤ i < p and 0 ≤ j < q. Group multiplication can be defined by a i b j ∗ a s b t = a i+s b jrs +t. In what follows, it will be convenient to refer to elements of a pq-group using the notation (i, j) instead of a i b j. 1 Ramsey Graphs Recall that an (s, t)-coloring of the complete graph Kn is a 2-coloring of its edges such that there is neither a complete subgraph of order s, all of whose edges are color 1, nor a complete subgraph of order t, all of whose edges are color 2. The Ramsey number R(s, t) is the minimum n such that no (s, t) coloring on Kn exists. Our first application of pq-groups gives us a new lower bound for R(4, 8). For this we use a Cayley coloring on the nonabelian group G of order 55, where we take p = 5, q = 11, and r = 3. Note that in a Cayley coloring, we assign 1 a color to each element g ∈ G, and then assign that color to edges of the form (x, xg), for all x ∈ G. In the array below the entry in row i, column j gives the color assigned to each element (i, j) i.e., a i b j, of G. It can be verified that this indeed determines a (4, 8)-coloring of K55, thereby improving the lower bound on R(4, 8) to 56 [4]
Some New Ramsey Colorings
No full textNew lower bounds for 15 classical Ramsey numbers are established. Several of the colorings are found using a new variation of local search heuristics. Several others are found using known colorings as building blocks. AMS Subject Classifications: 05D10, 05D04 Introduction In this note, several lower bounds for classical Ramsey numbers are improved using two different methods. First we use a new synthesis of simulated annealing and tabu search to establish several new bounds. Then some constructions that use smaller constructions as building blocks are described. In total, we improve 13 entries in Radziszowski's table of two-color classical Ramsey numbers [5], and also add two entries to his list of classical multicolor bounds. A Simple Search Algorithm The algorithm is outlined in the context of minimizing an integer function of binary (boolean) variables. Let f = f(x 1 ; : : : ; x k ) be such a function. Three important data structures are required: a current solution vector, a hi..
Variations on the Author
Full text link“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
On Voltage Graphs and Cages
No full textUsing voltage graphs, we construct the the smallest known trivalent graph of girth 16. The graph has 960 vertices and is a lift of the Petersen graph. By way of preparation, other lifts of the Petersen graph are discussed
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