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Opis: 2-colored quasi best match graphs (2-qBMGs) are directed graphs that arose in evolution theory. Investigations of 2-qBMGs have mostly focused on computational issues. However, 2-qBMGs also have relevant properties for structural graph theory; in particular, their undirected underlying graph is free from induced paths and cycles of size at least 6. In this paper, results on the structure of the automorphism groups of 2-qBMGs are obtained, which shows how to construct 2-qBMGs with large automorphism groups.
Ključne besede: group of automorphisms, bipartite graphs, phylogenetics
Objavljeno v RUP: 05.01.2026; Ogledov: 408; Prenosov: 1
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Ključne besede: distance-balanced graphs, quasi-distance-balanced graphs, bipartite graphs, bridge, razdaljno-uravnoteženi grafi, kvazi-razdaljno-uravnoteženi grafi, dvodelni grafi, most
Objavljeno v RUP: 07.02.2018; Ogledov: 10274; Prenosov: 148
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Opis: 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.
Ključne besede: graph theory, connected graphs, connectivity, distance-balanced graphs, bipartite graphs
Objavljeno v RUP: 15.10.2013; Ogledov: 9850; Prenosov: 103
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