Dve Laplasove energije i odnosi među njima
Sažetak
Uvod/cilj: Laplasova energija (LE) jeste suma apsolutnih vrednosti pojmova μi-2m/n, gde su μi, i=1,2,...,n, sopstvene vrednosti Laplasove matrice grafa G sa n vrhova i m ivica. Godine 2006. uvedena je druga veličina Z, zasnovana na Laplasovim svojstvenim vrednostima, koja je takođe nazvana „Laplasova energija”. Z je suma kvadrata Laplasovih svojstvenih vrednosti. Cilj ovog rada je nalaženje odnosa između LE i Z.
Rezultati: Donja i gornja granica za LE određene su kao funkcije od Z.
Zaključak: Rad doprinosi Laplasovoj spektralnoj teoriji i teoriji energije grafova. Pokazano je da je, kao gruba aproksimacija, LE proporcionalna sa (Z-4m2/n)1/2.
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