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URL:/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-frederico-cancado
SUMMARY:Algebraic Graph Theory-Frederico Cançado
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE: Quotient graphs and stochastic matrices\n\nS
 PEAKER:\n Frederico Cançado\n\nAFFILIATION:\n Universidade federal de Min
 as gerais \n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\
 nABSTRACT: Whenever graphs admit equitable partitions\, their quotient\ngr
 aphs highlight 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 according to certain equitable partitions. This\nquestion has bee
 n connected to the theory of fractional isomorphisms\nand covers of graphs
  in well-known results that we briefly presents in\nthese slides. We then 
 depart to develop theory of what happens when\nthe two graphs have the sam
 e symmetrized quotient\, proving a\nstructural result connecting this with
  the existence of certain doubly\nstochastic matrices. We apply this theor
 em to derive a new\ncharacterization of when two graphs have the same comb
 inatorial\nquotient\, and we also study graphs with weighted vertices and 
 the\nrelated concept of pseudo-equitable partitions. Our results connect t
 o\nknown old and recent results\, and are naturally applicable to study\nq
 uantum walks.\n 
DTSTAMP:20250714T054051Z
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