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1.
On the connectivity of bipartite distance-balanced graphs
Štefko Miklavič, Primož Šparl, 2012, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...A connected graph ▫$\varGamma$▫ is said to be distance-balanced whenever...
Keywords: graph theory, connected graphs, connectivity, distance-balanced graphs, bipartite graphs
Published: 15.10.2013; Views: 1398; Downloads: 52
URL Full text (0,00 KB)

2.
On bipartite Q-polynomial distance-regular graphs with c[sub]2 le 2
Štefko Miklavič, Safet Penjić, 2014, original scientific article

Found in: ključnih besedah
Summary of found: ...bipartite distance-regular graph, Q-polynomial property, equitable partition, ...
Keywords: bipartite distance-regular graph, Q-polynomial property, equitable partition
Published: 15.10.2015; Views: 1128; Downloads: 29
URL Full text (0,00 KB)

3.
On bipartite Q-polynomial distance-regular graphs with diameter 9, 10, or 11
Štefko Miklavič, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...bipartite distance-regular graph, Q-polynomial property, isomorphism...
Keywords: bipartite distance-regular graph, Q-polynomial property, isomorphism
Published: 12.03.2018; Views: 1214; Downloads: 23
URL Full text (0,00 KB)

4.
O Terwilligerjevi algebri dvodelnih razdaljno-regularnih grafov
Safet Penjić, 2019, doctoral dissertation

Found in: ključnih besedah
Summary of found: ... bipartite distance-regular graph, Terwilliger algebra, subconstituent algebra, Q-polynomi...
Keywords: bipartite distance-regular graph, Terwilliger algebra, subconstituent algebra, Q-polynomial property, equitable partition
Published: 04.06.2019; Views: 413; Downloads: 9
URL Full text (0,00 KB)

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