VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On the connectivity of bipartite distance-balanced graphs
    Miklavič, Štefko ; Šparl, Primož
    A connected graph ▫$\varGamma$▫ is said to be distance-balanced whenever for any pair of adjacent vertices ▫$u,v$▫ of ▫$\varGamma$▫ the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to ... the number of vertices closer to ▫$v$▫ than to ▫$u$▫. In [K. Handa, Bipartite graphs with balanced ▫$(a,b)$▫-partitions, Ars Combin. 51 (1999), 113-119] Handa asked whether every bipartite distance-balanced graph, that is not a cycle, is 3-connected. In this paper the Handa question is answered in the negative. Moreover, we show that a minimal bipartite distance-balanced graph, that is not a cycle and is not 3-connected, has 18 vertices and is unique. In addition, we give a complete classification of non-3-connected bipartite distance-balanced graphs for which the minimal distance between two vertices in a 2-cut is three. All such graphs are regular and for each ▫$k \geq 3$▫ there exists an infinite family of such graphs which are ▫$k$▫-regular.Furthermore, we determine a number of structural properties that a bipartite distance-balanced graph, which is not 3-connected, must have. As an application, we give a positive answer to the Handa question for the subfamily of bipartite strongly distance-balanced graphs.
    Vir: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 33, no. 2, 2012, str. 237-247)
    Vrsta gradiva - članek, sestavni del
    Leto - 2012
    Jezik - angleški
    COBISS.SI-ID - 1024369748

    Povezava(-e):

    http://dx.doi.org/10.1016/j.ejc.2011.10.002
    Repozitorij Univerze v Ljubljani – RUL
    Repozitorij Univerze na Primorskem - RUP

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