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Miguel Angel Fiol

Bio: Miguel Angel Fiol is an academic researcher from Polytechnic University of Catalonia. The author has contributed to research in topics: Regular graph & Distance-regular graph. The author has an hindex of 25, co-authored 150 publications receiving 2211 citations.


Papers
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Journal ArticleDOI
TL;DR: Substantial conditions are given, relating the diameter of G with its girth, to assure optimum values of these conditional connectivities of G.

275 citations

Journal ArticleDOI
TL;DR: This work studies the case in which all these components of a graph are different from a tree whose order is not greater than n, and some sufficient conditions for a graph to have the maximum possible conditional connectivity.

138 citations

Journal ArticleDOI
TL;DR: A new parameter I = I(G) is introduced for a loopless digraph G, which can be thought of as a generalization of the girth of a graph, and maximally connected and superconnected iterated line digraphs and (undirected) graphs are characterized.
Abstract: This paper introduces a new parameter I = I(G) for a loopless digraph G, which can be thought of as a generalization of the girth of a graph. Let k, λ, δ, and D denote respectively the connectivity, arc-connectivity, minimum degree, and diameter of G. Then it is proved that λ = δ if D ⩽ 2I and κ k = δ if D ⩽ 2I - 1. Analogous results involving upper bounds for k and λ are given for the more general class of digraphs with loops. Sufficient conditions for a digraph to be super-λ and super-k are also given. As a corollary, maximally connected and superconnected iterated line digraphs and (undirected) graphs are characterized.

136 citations

Journal ArticleDOI
TL;DR: The spectrum of the binary hypertree T"m (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct.

96 citations

Journal ArticleDOI
TL;DR: It is found out that there are no genuine “global” pseudo-distance-regular graphs: when pseudo- Distance-Regularity is shared by all the vertices, the graph turns out to be distance-regular.

86 citations


Cited by
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Book
05 Aug 2002
TL;DR: Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.
Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

1,938 citations

Book ChapterDOI
01 Jan 2007

1,089 citations

Journal ArticleDOI
TL;DR: The clinical expert consensus document part I summarizes the current state of knowledge on clinical presentation and characteristics of TTS and agrees on controversies surrounding TTS such as nomenclature, different TTS types, role of coronary artery disease, and etiology.
Abstract: Takotsubo syndrome (TTS) is a poorly recognized heart disease that was initially regarded as a benign condition. Recently, it has been shown that TTS may be associated with severe clinical complications including death and that its prevalence is probably underestimated. Since current guidelines on TTS are lacking, it appears timely and important to provide an expert consensus statement on TTS. The clinical expert consensus document part I summarizes the current state of knowledge on clinical presentation and characteristics of TTS and agrees on controversies surrounding TTS such as nomenclature, different TTS types, role of coronary artery disease, and etiology. This consensus also proposes new diagnostic criteria based on current knowledge to improve diagnostic accuracy.

903 citations

Book ChapterDOI
31 Dec 1939

811 citations

Dissertation
01 Jul 2001
TL;DR: This paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest LaPLacian eigenvalue λ2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph.
Abstract: The paper is essentially a survey of known results about the spectrum of the Laplacian matrix of graphs with special emphasis on the second smallest Laplacian eigenvalue λ2 and its relation to numerous graph invariants, including connectivity, expanding properties, isoperimetric number, maximum cut, independence number, genus, diameter, mean distance, and bandwidth-type parameters of a graph. Some new results and generalizations are added. † This article appeared in “Graph Theory, Combinatorics, and Applications”, Vol. 2, Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Schwenk, Wiley, 1991, pp. 871–898. ‡ The work supported in part by the Research Council of Slovenia, Yugoslavia. Part of the work was done while the author was a Fulbright Scholar at the Ohio State University, Columbus, Ohio.

717 citations