| Naslov: | Generalized stepwise transmission irregular graphs |
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| Avtorji: | ID Alizadeh, Yaser (Avtor)
ID Klavžar, Sandi (Avtor)
ID Molaee, Zohre (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (220,67 KB)
MD5: 78371CFD9EDCAD1A144A84861830DA2F
 URL - Izvorni URL, za dostop obiščite https://doiserbia.nb.rs/Article.aspx?ID=0354-51802416875A
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | The transmission ${\rm Tr}_G(u)$ of a vertex $u$ of a connected graph $G$ is the sum of distances from $u$ to all other vertices. $G$ is a stepwise transmission irregular (STI) graph if $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= 1$ holds for any edge $uv\in E(G)$. In this paper, generalized STI graphs are introduced as the graphs $G$ such that for some $k\ge 1$ we have $|{\rm Tr}_G(u) - {\rm Tr}_G(v)|= k$ for any edge $uv$ of $G$. It is proved that generalized STI graphs are bipartite and that as soon as the minimum degree is at least $2$, they are $2$-edge connected. Among the trees, the only generalized STI graphs are stars. The diameter of STI graphs is bounded and extremal cases discussed. The Cartesian product operation is used to obtain highly connected generalized STI graphs. Several families of generalized STI graphs are constructed. |
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| Ključne besede: | graph distance, transmission of vertex, stepwise transmission irregular graph, Cartesian product of graphs |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | str. 5875-5883 |
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| Številčenje: | Vol. 38, no. 16 |
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| PID: | 20.500.12556/DiRROS-24717  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 0354-5180 |
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| DOI: | 10.2298/FIL2416875A |
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| COBISS.SI-ID: | 212465411 |
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| Datum objave v DiRROS: | 15.12.2025 |
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| Število ogledov: | 10 |
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| Število prenosov: | 6 |
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| Metapodatki: |    |
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