| Naslov: | The ▫$\sigma$▫-irregularity of trees with maximum degree ▫$5$▫ |
|---|
| Avtorji: | ID Dimitrov, Darko (Avtor)
ID Kovijanić-Vukićević, Žana (Avtor)
ID Popivoda, Goran (Avtor)
ID Sedlar, Jelena (Avtor)
ID Škrekovski, Riste (Avtor)
ID Vujošević, Saša (Avtor) |
|---|
| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://www.sciencedirect.com/science/article/pii/S0166218X25006857
 PDF - Predstavitvena datoteka, prenos (679,47 KB)
MD5: 376E48E44FF580DB7A28FE572333A1C8
|
|---|
| Jezik: | Angleški jezik |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: |  RUDOLFOVO - Rudolfovo – Znanstveno in tehnološko središče Novo mesto
|
|---|
| Povzetek: | The ▫$\sigma$▫-irregularity, a variant of the well-established Albertson irregularity, is a topological invariant defined for a graph ▫$G=(V,E)$▫ as ▫$\sigma (G) = \sum_{u,v \in E}(d(u) - d(v))^2$▫, where ▫$d(u)$▫ and ▫$d(v)$▫ denote the degrees of vertices ▫$u$▫ and ▫$v$▫, respectively. Recent research has successfully characterized chemical trees with the maximum ▫$\sigma$▫-irregularity. In this paper, we expand upon this research by establishing several structural properties of maximal trees with prescribed maximum degree ▫$\Delta$▫. Application of these properties enables us to characterize maximal trees with ▫$\Delta = 5$▫. We establish that extremal trees contain only vertices of degrees ▫$1$▫, ▫$2$▫ and ▫$\Delta$▫. Moreover, the number of edges with both end-vertices having the degree ▫$2$▫ or ▫$\Delta$▫ is very small, so almost all edges have the (second) maximum possible contribution to ▫$\sigma$▫-irregularity. We believe this property or similar should extend to maximal trees for any value of ▫$\Delta$▫, so this is an interesting direction for further research. |
|---|
| Ključne besede: | regular graph, trees, maximum degree, [sigma]-irregularity, maximal graphs, graph measure, topological index |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija publikacije: | Objavljena publikacija |
|---|
| Datum objave: | 01.03.2026 |
|---|
| Založnik: | Elsevier |
|---|
| Leto izida: | 2026 |
|---|
| Št. strani: | str. 124-136 |
|---|
| Številčenje: | Vol. 382 |
|---|
| PID: | 20.500.12556/DiRROS-27405  |
|---|
| UDK: | 519.17 |
|---|
| ISSN pri članku: | 0166-218X |
|---|
| DOI: | 10.1016/j.dam.2025.11.045 |
|---|
| COBISS.SI-ID: | 266933507 |
|---|
| Avtorske pravice: | © 2025 The Authors |
|---|
| Opomba: | Žana Kovijanić Vukićević, Goran Popivoda, Jelena Sedlar, Riste Škrekovski, Saša Vujošević;
|
|---|
| Datum objave v DiRROS: | 05.02.2026 |
|---|
| Število ogledov: | 55 |
|---|
| Število prenosov: | 19 |
|---|
| Metapodatki: |    |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
