Search results for "Power graph"
showing 5 items of 5 documents
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
2006
A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…
The chronnectome of musical beat
2020
Keeping time is fundamental for our everyday existence. Various isochronous activities, such as locomotion, require us to use internal timekeeping. This phenomenon comes into play also in other human pursuits such as dance and music. When listening to music, we spontaneously perceive and predict its beat. The process of beat perception comprises both beat inference and beat maintenance, their relative importance depending on the salience of beat in the music. To study functional connectivity associated with these processes in a naturalistic situation, we used functional magnetic resonance imaging to measure brain responses of participants while they were listening to a piece of music contai…
Extracting business information from graphs: An eye tracking experiment
2016
Information graphics are visualizations that convey information about data trends and distributions. Data visualization and the application of graphs is increasingly important in business decision making, for instance, in big data analysis. However, relatively little information exists about how people extract information from graphs and how the framing of the graphic design defines may ‘nudge’ and bias decision making. As a contribution to fill this gap, this study applies the methodology of experimental economics to the analysis of graph reading and processing to extract underlying information. Specifically, the study presents the results of an experiment whose baseline treatment includes…
Empirical and theoretical study of atelostomate (Echinoidea, Echinodermata) plate architecture: using graph analysis to reveal structural constraints.
2015
AbstractDescribing patterns of connectivity among organs is essential for identifying anatomical homologies among taxa. It is also critical for revealing morphogenetic processes and the associated constraints that control the morphological diversification of clades. This is particularly relevant for studies of organisms with skeletons made of discrete elements such as arthropods, vertebrates, and echinoderms. Nonetheless, relatively few studies devoted to morphological disparity have considered connectivity patterns as a level of morphological organization or developed comparative frameworks with proper tools. Here, we analyze connectivity patterns among apical plates in Atelostomata, the m…
The b-chromatic number of power graphs
2003
The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.