| Title: | The conjecture on distance-balancedness of generalized Petersen graphs holds when internal edges have jumps $3$ or $4$ |
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| Authors: | ID Ma, Gang (Author)
ID Wang, JianFeng (Author)
ID Klavžar, Sandi (Author) |
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| Files: |  PDF - Presentation file, download (543,23 KB)
MD5: 6F281799BD158E2639752E01A1169815
 URL - Source URL, visit https://inmabb.criba.edu.ar/revuma/revuma.php?p=doi/v68n2a18
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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: | A connected graph $G$ with ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. Miklavič and Šparl [Discrete Appl. Math. 244 (2018), 143--154] conjectured that if $n > n_k$ where where $n_k = 11$ if $k = 2$, $n_k = (k+1)^2$ if $k$ is odd, and $n_k = k(k +2)$ if $k \ge 4$ is even, then the generalized Petersen graph $GP(n,k)$ is not $\ell$-distance-balanced for any $1\le \ell<{\rm diam}(GP(n,k))$. In the seminal paper, the conjecture was verified for $k=2$. In this paper we prove that the conjecture holds for $k=3$ and for $k=4$. |
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| Keywords: | distance-balanced graph, $\ell$-distance-balanced graph, generalized Petersen graph, diameter |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 703-733 |
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| Numbering: | Vol. 68, no. 2 |
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| PID: | 20.500.12556/DiRROS-24018  |
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| UDC: | 519.17 |
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| ISSN on article: | 1669-9637 |
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| DOI: | 10.33044/revuma.4824 |
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| COBISS.SI-ID: | 256284675 |
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| Note: |
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| Publication date in DiRROS: | 07.11.2025 |
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| Views: | 172 |
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| Downloads: | 90 |
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