ǂA ǂtheorem on Wiener-type invariants for isometric subgraphs of hypercubes

Sandi Klavžar (Author), Ivan Gutman (Author)

Abstract

Naj bo ▫$d(G,k)$▫ število parov točk grafa ▫$G$▫, ki so na razdalji ▫$k$▫, naj bo ▫$\lambda$▫ realno (ali kompleksno) število in naj bo ▫$W_\lambda(G) =\sum_{k \ge 1}d(G,k)k^\lambda$▫. Dokazano je, da za delno kocko ▫$G$▫ velja ▫$W_{\lambda + 1}(G) = |\mathcal{F}| W_\lambda(G) - \sum_{\mathnormal{F} \in \mathcal{F}} W_\lambda(G \setminus F)$▫, kjer je ▫$\mathcal{F}$▫ particija ▫$E(G)$▫, ki jo inducira Djokovic-Winklerjeva relacija ▫$\Theta$▫. Ta rezultat razširja prej znani rezultat za drevesa in implicira različne relacije za topološke indekse, ki temeljijo na razdaljah.

Keywords

matematika;teorija grafov;grafovska razdalja;hiperkocka;delna kocka;Wienerjevo število;hiper-Wienerjev indeks;mathematics;graph theory;graph distance;hypercube;partial cube;Wiener number;hyper-Wiener indeks;

Data

Language:	English
Year of publishing:	2006
Typology:	1.01 - Original Scientific Article
Organization:	UM PEF - Faculty of Education
UDC:	519.17
COBISS:	14040665
ISSN:	0893-9659
Views:	37
Downloads:	29
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Izrek o invariantah Wienerjevega tipa za izometrične podgrafe hiperkock
Secondary abstract:	Let ▫$d(G,k)$▫ be the number of pairs of vertices of a graph ▫$G$▫ that are at distance ▫$k$▫, ▫$\lambda$▫ a real (or complex) number, and ▫$W_\lambda(G) = \sum_{k \ge 1}d(G,k)k^\lambda$▫. It is proved that for a partial cube ▫$G$▫, ▫$W_{\lambda + 1}(G) = \|\mathcal{F}\| W_\lambda(G) - \sum_{\mathnormal{F} \in \mathcal{F}} W_\lambda(G \setminus F)$▫ where ▫$\mathcal{F}$▫ is the partition of ▫$E(G)$▫ induced by the Djokovic-Winkler relation ▫$\Theta$▫. This result extends a previously known result for trees and implies several relations for distance-based topological indices.
Secondary keywords:	matematika;teorija grafov;grafovska razdalja;hiperkocka;delna kocka;Wienerjevo število;hiper-Wienerjev indeks;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1129-1133
Volume:	ǂVol. ǂ19
Issue:	ǂiss. ǂ10
Chronology:	2006
ID:	1472813