Walk-generating functions and spectral measures of infinite graphs
Godsil, Christopher David, 1949- ; Mohar, Bojan, 1956-
Naj bo ▫$A$▫ operator sosednosti lokalno končnega neskončnega grafa ▫$G$▫. Naj bo ▫$E(\lambda)$▫ razbitje enote za ▫$A$▫ in ▫$e_v$▫, ▫$v\in V(G)$▫, Hilbertova baza prostora ▫$\ell^2(V(G))$▫. ...Spektralna mera je funkcija ▫$\mu_{mv}(\lambda) = (E(\lambda)e_u, e_v)$▫ in je v tesni zvezi z rodovno funkcijo za število sprehodov dane dolžine od ▫$u$▫ do ▫$v$▫. S pomočjo spektralnih so dokazani naslednji rezultati: karakterizacija dvodelnih grafov na podlagi spektra, posplošitev Plancherelove mere za grafe, ki niso nujno Cayleyevi, izreki o konvergenci spektralnih mer, porazdelitev spektra slučajnih končnih regularnih ali dvodelnih semiregularnih grafov, nove metode za določanje spektralnih mer nekaterih družin grafov.
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