| Title: | Semicubic cages and small graphs of even girth from voltage graphs |
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| Authors: | ID Aguilar, Flor (Author)
ID Araujo-Pardo, Gabriela (Author)
ID Berman, Leah (Author) |
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| Files: |  AMC__Aguilar,_Araujo-Pardo,_Berman_2026.pdf (574,36 KB)
MD5: 2C052305463C4C1BBAA520CB216BA3C5
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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: | A ({3, m}; g)-semicubic graph is a graph where the degree of each vertex is either 3 or m and the girth of the graph is g; if m = 3 we have a cubic graph. In this paper, we construct families of semicubic graphs of even girth and small order using two different techniques. The first technique generalizes a previous construction, which glues cubic cages of girth g together at remote vertices (vertices at distance at least g/2). The second technique, the main content of this paper, produces bipartite semicubic ({3, m}; g)-graphs of even girth g using voltage graphs over ℤm. For girth g = 4t + 2, t ≥ 1, the constructed graphs have two vertices of degree m. For girth g = 4t, t ≥ 2, the construction produces graphs with exactly three vertices of degree m (of course, the remaining vertices are of degree 3 in both cases). In particular, we describe infinite families of ({3, m}; g)−semicubic graphs for g = {6, 8, 10, 12} for infinitely many values of m. The cases g = {6, 8} include the unique 6-cage and the unique 8-cage when m = 3. The families obtained in this paper for girth g = {10, 12} include examples of orders that match the best-known bounds for ({3, m}; g)−semicubic graphs until this moment. |
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| Keywords: | Graph, semicubic graph, girth, voltage graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 02.06.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 30 str. |
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| Numbering: | Vol. 26, no. 3, [article no.] P3.03 |
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| PID: | 20.500.12556/RUP-23505  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3116.35e |
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| Publication date in RUP: | 17.08.2026 |
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| Views: | 85 |
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| Downloads: | 1 |
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