2,386 research outputs found
Upper bounds for the bondage number of graphs on topological surfaces
The bondage number b(G) of a graph G is the smallest number of edges of G
whose removal from G results in a graph having the domination number larger
than that of G. We show that, for a graph G having the maximum vertex degree
and embeddable on an orientable surface of genus h and a
non-orientable surface of genus k, . This generalizes known upper bounds for planar and toroidal
graphs.Comment: 10 pages; Updated version (April 2011); Presented at the 7th ECCC,
Wolfville (Nova Scotia, Canada), May 4-6, 2011, and the 23rd BCC, Exeter
(England, UK), July 3-8, 201
The bondage number of graphs on topological surfaces and Teschner's conjecture
The bondage number of a graph is the smallest number of its edges whose
removal results in a graph having a larger domination number. We provide
constant upper bounds for the bondage number of graphs on topological surfaces,
improve upper bounds for the bondage number in terms of the maximum vertex
degree and the orientable and non-orientable genera of the graph, and show
tight lower bounds for the number of vertices of graphs 2-cell embeddable on
topological surfaces of a given genus. Also, we provide stronger upper bounds
for graphs with no triangles and graphs with the number of vertices larger than
a certain threshold in terms of the graph genera. This settles Teschner's
Conjecture in positive for almost all graphs.Comment: 21 pages; Original version from January 201
Continuity, Discontinuity and Dynamics in Mathematics & Economics - Reconsidering Rosser's Visions
Barkley Rosser has been a pioneer in arguing the case for the mathematics of discontinuity, broadly conceived, to be placed at the foundations of modelling economic dynamics. In this paper we reconsider this vision from the broad perspective of a variety of different kinds of mathematics and suggest a broadening of Rosser’s methodology to the study of economic dynamicsContinuity, Discontinuity, Economic Dynamics, Relaxation Oscillations
Simulating HIV-1 Protease Mutations for Conferred Drug Resistance
A major challenge in the long-term management of HIV is drug resistance caused from high rate and error prone viral replication. To examine mechanisms of drug resistance within HIV-1 protease complexed with Darunavir, specific point mutations were placed in the protease amino acid sequence and molecular dynamic simulations were run. MATLAB and python scripts were developed to efficiently and consistently analyze simulation data. The team hypothesized that there would be a difference in inhibitor interactions and protein dynamic behavior in mutant variants compared to wild type. Although some aspects of increased resistance were seen with compounded mutations, overall this trend was not observed across every facet of our analysis
The possibility of evaluating vertical wind profiles from satellite data
There are no author-identified significant results in this report
Efficient total domination in digraphs
We generalize the concept of efficient total domination from graphs to digraphs. An efficiently total dominating set X of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor in X . Not every digraph has an efficiently total dominating set. We study graphs that permit an orientation having such a set and give complexity results and characterizations concerning this question. Furthermore, we study the computational complexity of the (weighted) efficient total domination problem for several digraph classes. In particular we deal with most of the common generalizations of tournaments, like locally semicomplete and arc-locally semicomplete digraphs
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