New bounds for the sum of powers of normalized Laplacian eigenvalues of graphs
Clemente, Gian Paolo ; Cornaro, Alessandra
Bozkurt in Bozkurt (2012) sta za enostaven in povezan graf vpeljala novo invarianto ▫$s_\alpha^\ast (G)$▫, definirano kot vsoto ▫$\alpha$▫ potenc lastnih vrednosti normalizirane Laplaceove matrike. ...Avtorja sta našla spodnje in zgornje meje za ta indeks. V tem članku lokaliziramo lastne vrednosti normalizirane Laplaceove matrike z uporabo teoretične metode, ki sta jo razvila Bianchi in Torriero (2000), in je osnovana na majorizacijskih tehnikah. S tem pristopom izpeljemo zgornje in spodnje meje za ▫$s_\alpha^\ast (G)$▫. Nekaj numeričnih primerov pokaže, kako je mogoče dobiti ostrejše rezultate v primerjavi s tistimi, ki obstajajo v litaraturi.
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