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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
Keywords: graph theory, connected graphs, connectivity, distance-balanced graphs, bipartite graphs
Published: 15.10.2013; Views: 1400; Downloads: 52
URL Full text (0,00 KB)

2.
On the readability of overlap digraphs
Rayan Chikhi, Paul Medvedev, Martin Milanič, Sofya Raskhodnikova, 2016, original scientific article

Found in: ključnih besedah
Summary of found: ... bipartite graphs, readability, overlap labeling, ...
Keywords: bipartite graphs, readability, overlap labeling
Published: 08.08.2016; Views: 1312; Downloads: 170
URL Full text (0,00 KB)

3.
On some properties of quasi-distance-balanced graphs
Ademir Hujdurović, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...distance-balanced graphs, quasi-distance-balanced graphs, bipartite graphs, bridge, razdaljno-uravnoteženi grafi, kvazi-razdaljno-uravnoteženi graf...
Keywords: distance-balanced graphs, quasi-distance-balanced graphs, bipartite graphs, bridge, razdaljno-uravnoteženi grafi, kvazi-razdaljno-uravnoteženi grafi, dvodelni grafi, most
Published: 07.02.2018; Views: 1482; Downloads: 85
URL Full text (0,00 KB)

4.
On biregular bipartite graphs of small excess
Slobodan Filipovski, Alejandra Ramos Rivera, Robert Jajcay, 2019, original scientific article

Found in: ključnih besedah
Keywords: biregular bipartite graphs, degree/girth problem, asymptotic density
Published: 22.05.2019; Views: 247; Downloads: 87
URL Full text (0,00 KB)

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