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On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphsAlizadeh, Yaser ; Klavžar, SandiČe je ▫$u$▫ vozlišče grafa ▫$G$▫, potem je celotna razdalja vozlišča ▫$u$▫ vsota razdalj od ▫$u$▫ do vseh ostalih vozlišč ▫$G$▫. Wienerjeva zahtevnost ▫$C_W(G)$▫ grafa ▫$G$▫ je število različnih ... celotnih razdalj njegovih vozlišč. ▫$G$▫ je razdaljno iregularen, če je ▫$C_W(G) = n(G)$▫. Dokazano je, da skoraj noben graf ni razdaljno iregularen. Naj bo ▫$T_{n_1,n_2,n_3}$▫ drevo, ki ga dobimo iz poti dolžin ▫$n_1$▫, ▫$n_2$▫ in ▫$n_3$▫ z identifikacijo po enega končnega vozlišča na njih. Dokazano je, da je ▫$T_{1,n_2,n_3}$▫ razdaljno iregularen natanko tedaj, ko je ▫$n_3 =n_2+1$▫ in ▫$n_2 \notin \left\{(k^2-1)/2, (k^2-2)/2\right\}$▫ za nek ▫$k \ge 3$▫. Dokazano je tudi, da je če je ▫$T$▫ asimetrično drevo reda ▫$n$▫, potem je Wienerjev indeks drevesa ▫$T$▫ omejen z ▫$(n^3 - 13n + 48)/6$▫. Pri tem enakost velja natanko tedaj, ko je ▫$T = T_{1,2,n-4}$▫. Dokazan je vzporeden rezultat za asimetrične enociklične grafe.Source: Applied mathematics and computation. - ISSN 0096-3003 (Vol. 328, July 2018, str. 113-118)Type of material - article, component part ; adult, seriousPublish date - 2018Language - englishCOBISS.SI-ID - 18255705
Author
Alizadeh, Yaser |
Klavžar, Sandi
Topics
Wienerjev indeks |
Wienerjeva zahtevnost |
asimetrični graf |
enociklični grafi |
Wiener index |
Wiener complexity |
asymmetric graphs |
trees |
uni-cyclic graphs
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Database name | Field | Year |
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Alizadeh, Yaser | |
Klavžar, Sandi | 05949 |
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