| Title: | On edge-girth-regular graphs: lower bounds and new families |
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| Authors: | ID Porupsánszki, István (Author) |
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| Files: |  AMC_Porupsanszki_2025.pdf (358,49 KB)
MD5: E735666385C53AA8C42F4E97D01ED175
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | An edge-girth-regular graph egr(n, k, g, λ) is a k-regular graph of order n, girth g and with the property that each of its edges is contained in exactly λ distinct g-cycles. We present new families of edge-girth regular graphs arising from generalized quadrangles and pencils of elliptic quadrics.
An egr(n, k, g, λ) is called extremal for the triple (k, g, λ) if n is the smallest order of any egr(n, k, g, λ). We give new lower bounds for the order of extremal edge-girth-regular graphs using properties of the eigenvalues of the adjacency matrix of a graph. |
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| Keywords: | cage problem, extremal graph theory, generalized polygons, ovoids |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 22.08.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 15 str. |
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| Numbering: | Vol. 25, no. 4, [article no.] P4.07 |
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| PID: | 20.500.12556/RUP-22020  |
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| UDC: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3107.9df |
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| Publication date in RUP: | 22.10.2025 |
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| Views: | 336 |
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| Downloads: | 1 |
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