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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20241216T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-frederico-cancado
SUMMARY:Algebraic Graph Theory-Frederico Cançado
CLASS:PUBLIC
DESCRIPTION:TITLE: Quotient graphs and stochastic matrices\n\nSPEAKER:\n Fr
 ederico Cançado\n\nAFFILIATION:\n Universidade federal de Minas gerais \
 n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRACT: W
 henever graphs admit equitable partitions\, their quotient\ngraphs highlig
 ht the structure evidenced by the partition. It is\ntherefore very natural
  to ask what can be said about two graphs that\nhave the same quotient acc
 ording to certain equitable partitions. This\nquestion has been connected 
 to the theory of fractional isomorphisms\nand covers of graphs in well-kno
 wn results that we briefly presents in\nthese slides. We then depart to de
 velop theory of what happens when\nthe two graphs have the same symmetrize
 d quotient\, proving a\nstructural result connecting this with the existen
 ce of certain doubly\nstochastic matrices. We apply this theorem to derive
  a new\ncharacterization of when two graphs have the same combinatorial\nq
 uotient\, and we also study graphs with weighted vertices and the\nrelated
  concept of pseudo-equitable partitions. Our results connect to\nknown old
  and recent results\, and are naturally applicable to study\nquantum walks
 .
DTSTAMP:20260403T082929Z
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