Extremal Edge-Girth-Regular Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10248248" target="_blank" >RIV/61989100:27240/21:10248248 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00373-021-02368-9" target="_blank" >https://link.springer.com/article/10.1007%2Fs00373-021-02368-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00373-021-02368-9" target="_blank" >10.1007/s00373-021-02368-9</a>

Result language
angličtina
Original language name
Extremal Edge-Girth-Regular Graphs
Original language description
An edge-girth-regular egr(v, k, g, λ)-graph Γ is a k-regular graph of order v and girth g in which every edge is contained in λ distinct g-cycles. Edge-girth-regularity is shared by several interesting classes of graphs which include edge- and arc-transitive graphs, Moore graphs, as well as many of the extremal k-regular graphs of prescribed girth or diameter. Infinitely many egr(v, k, g, λ)-graphs are known to exist for sufficiently large parameters (k, g, λ), and in line with the well-known Cage Problem we attempt to determine the smallest graphs among all edge-girth-regular graphs for given parameters (k, g, λ). To facilitate the search for egr(v, k, g, λ)-graphs of the smallest possible orders, we derive lower bounds in terms of the parameters k, g and λ. We also determine the orders of the smallest egr(v, k, g, λ)-graphs for some specific parameters (k, g, λ), and address the problem of the smallest possible orders of bipartite edge-girth-regular graphs.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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