| Title: | Generalized stepwise transmission irregular graphs |
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| Authors: | ID Alizadeh, Yaser (Author)
ID Klavžar, Sandi (Author)
ID Molaee, Zohre (Author) |
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| Files: |  PDF - Presentation file, download (220,67 KB)
MD5: 78371CFD9EDCAD1A144A84861830DA2F
 URL - Source URL, visit https://doiserbia.nb.rs/Article.aspx?ID=0354-51802416875A
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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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| Keywords: | graph distance, transmission of vertex, stepwise transmission irregular graph, Cartesian product of graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 5875-5883 |
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| Numbering: | Vol. 38, no. 16 |
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| PID: | 20.500.12556/DiRROS-24717  |
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| UDC: | 519.17 |
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| ISSN on article: | 0354-5180 |
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| DOI: | 10.2298/FIL2416875A |
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| COBISS.SI-ID: | 212465411 |
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| Publication date in DiRROS: | 15.12.2025 |
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| Views: | 9 |
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| Downloads: | 6 |
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| Metadata: |    |
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