Distance-balanced graphs
Abstract
V članku so vpeljani razdaljno uravnoteženi grafi kot grafi, v katerih ima vsaka povezava ▫$uv$▫ naslednjo lastnost: število točk, ki so bližje ▫$u$▫ kot ▫$v$▫, je enako kot število točk, ki so bližje ▫$v$▫ kot ▫$u$▫. Dobljene so osnovne lastnosti teh grafov. Novi koncept je povezan z grafovskimi simetrijami, študirane so tudi lokalne operacije na grafih glede na razdaljno uravnoteženost. Karakterizirani so razdaljno uravnoteženi kartezični in leksikografski produkti grafov. Postavljenih je več odprtih problemov.
Keywords
matematika;teorija grafov;razdalja;razdaljno uravnoteženi grafi;produkti grafov;povezanost;mathematics;graph theory;graph distance;distance-balanced graphs;graph products;connectivity;
Data
| Language: | English |
|---|---|
| Year of publishing: | 2005 |
| Typology: | 0 - Not set |
| Organization: | UM PEF - Faculty of Education |
| UDC: | 519.17 |
| COBISS: |
13785689
|
| ISSN: | 1318-4865 |
| Views: | 1053 |
| Downloads: | 80 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | Unknown |
|---|---|
| Secondary title: | Razdaljno uravnoteženi grafi |
| Secondary abstract: | Distance-balanced graphs are introduced as graphs in which every edge $uv$ has the following property: the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. Basic properties of these graphs are obtained. The new concept is connected with symmetry conditions in graphs and local operations on graphs are studied with respect to it. Distance-balanced Cartesian and lexicographic products of graphs are also characterized. Several open problems are posed along the way. |
| Secondary keywords: | matematika;teorija grafov;razdalja;razdaljno uravnoteženi grafi;produkti grafov;povezanost; |
| URN: | URN:SI:UM: |
| Type (COBISS): | Not categorized |
| Pages: | str. 1-9 |
| Volume: | ǂVol. ǂ43 |
| Issue: | ǂšt. ǂ992 |
| Chronology: | 2005 |
| ID: | 66677 |
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