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DTSTART;TZID=UTC:20220309T153000
DTEND;TZID=UTC:20220309T163000
DTSTAMP:20260616T090008
CREATED:20220307T121100Z
LAST-MODIFIED:20220307T122041Z
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SUMMARY:Atlantic Graph Theory Seminar: Pjotr Buys (University of Amdsterdam)
DESCRIPTION:About a year ago Jason Brown spoke in our seminar (of the university of Amsterdam) about the two-terminal reliability polynomial and left us with some questions about the closure of the complex zeros of all such polynomials (the zero-locus). In this talk I will define a way to capture\, for a certain parameter\, whether the set of all two-terminal reliability polynomials behaves chaotically around this parameter or not\, i.e. whether this parameter is active or passive. I call the set of all active parameters the activity-locus and I will show that it is equal to the zero-locus. I will use this framework to prove some fun things about the zero-locus. Although I have not yet figured out how to use this to answer any of the open questions posed by Jason\, I am hopeful it might be a step in the right direction. \n\nJoin Zoom Meeting: link
URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-pjotr-nuys-university-of-amdsterdam/
LOCATION:Online via Zoom
CATEGORIES:AARMS Atlantic Graph Theory Seminar
ORGANIZER;CN="Jason Brown":MAILTO:jason.brown@dal.ca
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DTSTART;TZID=UTC:20220316T153000
DTEND;TZID=UTC:20220316T163000
DTSTAMP:20260616T090008
CREATED:20220314T110128Z
LAST-MODIFIED:20220314T110138Z
UID:6626-1647444600-1647448200@aarms.math.ca
SUMMARY:Atlantic Graph Theory Seminar: Theodore Kolokolnikov (Dalhousie)
DESCRIPTION:We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs\, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution. For an integer d in [3\,8]\, we find families of random semi-regular graphs that have higher algebraic connectivity than a random d-regular graphs with the same number of vertices and edges. On the other hand\, we show that regular graphs beat semi-regular graphs when d >8. More generally\, we study random semi-regular graphs whose average degree is d\, not necessary an integer. This provides a natural generalization of a d-regular graph in the case of a non-integer d. We characterise their algebraic connectivity in terms of a root of a certain 6th-degree polynomial. Finally\, we construct a small-world-type network of average degree 2.5 with a relatively high algebraic connectivity. We also propose some related open problems and conjectures.
URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-theodore-kolokolnikov-dalhousie/
LOCATION:Online via Zoom
CATEGORIES:AARMS Atlantic Graph Theory Seminar
ORGANIZER;CN="Jason Brown":MAILTO:jason.brown@dal.ca
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