1,721,012 research outputs found
A Lexicographic product for Signed Graphs
Full text linkA signed graph is a pair = (G; ), where G = (V (G);E(G)) is a graph
and E(G) {+1;−1} is the sign function on the edges of G. The
notion of composition (also known as lexicographic product) of two signed
graphs and = (H; ) already exists in literature, yet it fails to map
balanced graphs onto balanced graphs. We improve the existing denition
showing that our `new' signature on the lexicographic product of G and
H behaves well with respect to switching equivalence. Signed regularities
and some spectral properties are also discussed
On a class of poly-context-free groups generated by automata
Full text linkThis paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is isomorphic to the partially commutative monoid associated with the complement of the line graph of the defining tree. After that, we generalize these groups by introducing the quite broad class of reducible automaton groups, which lies in the class of contracting automaton groups without singular points. We give a general structure theorem that shows that all reducible automaton groups are direct limits of poly-context -free groups which are virtually subgroups of the direct product of free groups; notice that this result partially supports a conjecture by T. Brough. Moreover, we prove that tree automaton groups with at least two generators are not finitely presented and they are amenable groups, which are direct limit of non-amenable groups
Construction of cospectral graphs, signed graphs and T-gain graphs via partial transpose
No full textIn the wake of Dutta and Adhikari, who in 2020 used partial transposition in order to get pairs of cospectral graphs, we investigate partial transposition for Hermitian complex matrices. This allows us to construct infinite pairs of complex unit gain graphs (or T-gain graphs) sharing either the spectrum of the adjacency matrix or even the spectrum of all the generalized adjacency matrices. This investigation also sheds new light on the classical case, producing examples that were still missing even for graphs. Partial transposition requires a block structure of the matrix: we interpreted it as if coming from a composition of T-gain digraphs. By proposing a suitable definition of rigidity specifically for T-gain digraphs, we then produce the first examples of pairs of non-isomorphic graphs, signed graphs and T-gain graphs obtained via partial transposition of matrices whose blocks form families of commuting normal matrices. In some cases, the non-isomorphic graphs detected in this way turned out to be hardly distinguishable, since they share the adjacency, the Laplacian and the signless Laplacian spectrum, together with many non-spectral graph invariants
Constructing cospectral signed graphs
No full textA well-known fact in Spectral Graph Theory is the existence of pairs of cospectral (or isospectral) nonisomorphic graphs, known as PINGS. The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of cospectral graphs, and they gave routines to construct PINGS. Here, we consider the Godsil–McKay-type routines developed for graphs, whose adjacency matrices are (Formula presented.) -matrices, to the level of signed graphs, whose adjacency matrices allow the presence of (Formula presented.) s. We show that, with suitable adaption, such routines can be successfully ported to signed graphs, and we can build pairs of cospectral switching nonisomorphic signed graphs
Graph automaton groups
Full text linkIn this paper we define a way to get a bounded invertible automaton starting from a finite graph. It turns out that the corresponding automaton group is regular weakly branch over its commutator subgroup, contains a free semigroup on two elements and is amenable of exponential growth. We also highlight a connection between our construction and the right-angled Artin groups. We then study the Schreier graphs associated with the self-similar action of these automaton groups on the regular rooted tree. We explicitly determine their diameter and their automorphism group in the case where the initial graph is a path. Moreover, we show that the case of cycles gives rise to Schreier graphs whose automorphism group is isomorphic to the dihedral group. It is remarkable that our construction recovers some classical examples of automaton groups like the Adding machine and the Tangled odometer. Mathematics Subject Classification (2020): 20F65, 20F05, 20E08, 05C10, 05C25
Godsil-McKay switching for mixed and gain graphs over the circle group
No full textIn this paper we describe two methods, both inspired from Godsil-McKay switching on simple graphs, to build cospectral gain graphs whose gain group consists of the complex numbers of modulus 1 (the circle group). The results obtained here can be also applied to the Hermitian matrix of mixed graphs
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
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
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