A theorem on Wiener-type invariants for isometric subgraphs of hypercubes

Klavžar, Sandi; Gutman, Ivan

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Title:	A theorem on Wiener-type invariants for isometric subgraphs of hypercubes
Authors:	ID Klavžar, Sandi (Author) ID Gutman, Ivan (Author)
Files:	http://dx.doi.org/10.1016/j.aml.2005.12.004
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	PEF - Faculty of Education
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
Year of publishing:	2006
Number of pages:	str. 1129-1133
Numbering:	Vol. 19, iss. 10
PID:	20.500.12556/DKUM-51558
UDC:	519.17
ISSN on article:	0893-9659
COBISS.SI-ID:	14040665
NUK URN:	URN:SI:UM:DK:VCCIRZ28
Publication date in DKUM:	10.07.2015
Views:	1388
Downloads:	126
Metadata:
Categories:	Misc.
:	KLAVŽAR, Sandi and GUTMAN, Ivan, 2006, A theorem on Wiener-type invariants for isometric subgraphs of hypercubes. Applied Mathematics Letters [online]. 2006. Vol. 19, no. 10, p. 1129–1133. [Accessed 4 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.aml.2005.12.004 Copy citation

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Record is a part of a journal

Title:	Applied Mathematics Letters
Shortened title:	Appl. math. lett.
Publisher:	Pergamon
ISSN:	0893-9659
COBISS.SI-ID:	24984320

Secondary language

Language:	Unknown
Title:	Izrek o invariantah Wienerjevega tipa za izometrične podgrafe hiperkock
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.

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