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  • Edge-girth-regular graphs
    Jajcay, Robert ; Kiss, György, matematik ; Miklavič, Štefko
    We consider a new type of regularity we call edge-girth-regularity. An edge-girth-regular ▫$(v, k, g, \lambda)$▫-graph ▫$\varGamma$▫ is a ▫$k$▫-regular graph of order ▫$v$▫ and girth ▫$g$▫ in which ... every edge is contained in ▫$\lambda$▫ distinct ▫$g$▫-cycles. This concept is a generalization of the well-known concept of ▫$(v, k, \lambda)$▫-edge-regular graphs (that count the number of triangles) and appears in several related problems such as Moore graphs and cage and degree/diameter problems. All edge- and arc-transitive graphs are edge-girth-regular as well. We derive a number of basic properties of edge-girth-regular graphs, systematically consider cubic and tetravalent graphs from this class, and introduce several constructions that produce infinite families of edge-girth-regular graphs. We also exhibit several surprising connections to regular embeddings of graphs in orientable surfaces.
    Source: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 72, Aug. 2018, str. 70-82)
    Type of material - article, component part ; adult, serious
    Publish date - 2018
    Language - english
    COBISS.SI-ID - 1540315332

    Link(s):

    https://www.sciencedirect.com/science/article/pii/S0195669818300787
    Repository of University of Primorska - RUP
    DOI

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