| Naslov: | Some results on ▫$\sigma_t$▫-irregularity |
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| Avtorji: | ID Filipovski, Slobodan (Avtor)
ID Dimitrov, Darko (Avtor)
ID Knor, Martin (Avtor)
ID Škrekovski, Riste (Avtor) |
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| Datoteke: |  RAZ_Filipovski_Slobodan_2026.pdf (335,30 KB)
MD5: 1A83748BA5C7D5BD8A6561F989D45AB7
 https://amc-journal.eu/index.php/amc/article/view/3268
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FAMNIT - Fakulteta za matematiko, naravoslovje in informacijske tehnologije
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| Opis: | The (\sigma_t)-irregularity (or sigma total index) is a graph invariant defined as [ \sigma_t(G)=\sum_{{u,v}\subseteq V(G)}(d(u)-d(v))^2, ] where (d(z)) denotes the degree of a vertex (z). This irregularity measure was proposed by Réti in 2019 and recently rediscovered by Dimitrov and Stevanović in 2023. In this paper, we remark that (\sigma_t(G)=n^2\operatorname{Var}(G)), where (\operatorname{Var}(G)) is the degree variance of the graph. We show that among all complete bipartite graphs on (n) vertices, one of the corresponding complete bipartite graphs whose part sizes are closest to (n(2-\sqrt{2})/4) and (n(2+\sqrt{2})/4) has the maximum sigma total index. Moreover, various upper and lower bounds for (\sigma_t)-irregularity are provided. In this direction, we establish a relation between the graph energy (\mathcal{E}(G)) and (\sigma_t)-irregularity and derive bounds related to the Laplacian eigenvalues of the graph. |
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| Ključne besede: | irregularity, total irregularity, energy of graphs, Laplacian eigenvalues |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 11.08.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | str. 1-12 |
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| Številčenje: | Vol. 26, no. 4, [article no.] P4.01 |
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| PID: | 20.500.12556/RUP-23481  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3268.60f |
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| COBISS.SI-ID: | 254097667 |
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| Datum objave v RUP: | 14.08.2026 |
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| Število ogledov: | 25 |
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| Število prenosov: | 2 |
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| Metapodatki: |    |
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