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Transitive, locally finite median graphs with finite blocks
Wilfried Imrich, Sandi Klavžar, 2008

Abstract: V članku obravnavamo neskončne, lokalno končne, vozliščno-tranzitivne medianske grafe. Pokazano je, da končnost ▫$Theta$▫-razredov takih grafov ne zagotavlja končnosti blokov. Bloki pa postanejo neskončni, če nadalje nobeno končno zaporedje ▫$Theta$▫-kontrakcij ne naredi novih prereznih vozlišč. Dokazano je, da obstaja končno mnogo vozliščno-tranzitivnih medianskih grafov fiksne stopnje, ki imajo končne bloke. Konstruirana je neskončna družina vozliščno-tranzitivnih medianskih grafov z intranzitivnimi bloki. Podan je tudi seznam vseh vozliščno-tranzitivnih medianskih grafov stopnje 4.
Keywords: teorija grafov, medianski grafi, neskočni grafi, vozliščno-tranzitivni grafi, graph theory, median graphs, infinite graphs, vertex-transitive graphs
Published: 10.07.2015; Views: 396; Downloads: 56
URL Link to full text

3.
Transitive, locally finite median graphs with finite blocks
Wilfried Imrich, Sandi Klavžar, 2009, original scientific article

Abstract: V članku obravnavamo neskončne, lokalno končne, vozliščno-tranzitivne medianske grafe. Pokazano je, da končnost ▫$Theta$▫-razredov takih grafov ne zagotavlja končnosti blokov. Bloki pa postanejo neskončni, če nadalje nobeno končno zaporedje ▫$Theta$▫-kontrakcij ne naredi novih prereznih vozlišč. Dokazano je, da obstaja končno mnogo vozliščno-tranzitivnih medianskih grafov fiksne stopnje, ki imajo končne bloke. Konstruirana je neskončna družina vozliščno-tranzitivnih medianskih grafov z intranzitivnimi bloki. Podan je tudi seznam vseh vozliščno-tranzitivnih medianskih grafov stopnje 4.
Keywords: teorija grafov, medianski grafi, neskočni grafi, vozliščno-tranzitivni grafi, graph theory, median graphs, infinite graphs, vertex-transitive graphs
Published: 10.07.2015; Views: 419; Downloads: 64
URL Link to full text

4.
Edge-transitive lexicographic and cartesian products
Wilfried Imrich, Ali Iranmanesh, Sandi Klavžar, Abolghasem Soltani, 2016, original scientific article

Abstract: In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product ▫$G \circ H$▫ of a connected graph ▫$G$▫ that is not complete by a graph ▫$H$▫, we show that it is edge-transitive if and only if ▫$G$▫ is edge-transitive and ▫$H$▫ is edgeless. If the first factor of ▫$G \circ H$▫ is non-trivial and complete, then ▫$G \circ H$▫ is edge-transitive if and only if ▫$H$▫ is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao (Appl. Math. Lett. 24 (2011) 1924--1926). For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph.
Keywords: edge-transitive graph, vertex-transitive graph, lexicographic product of graphs, Cartesian product of graphs
Published: 31.03.2017; Views: 320; Downloads: 201
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5.
The Hosoya-Wiener polynomial of weighted trees
Blaž Zmazek, Janez Žerovnik, 2007, original scientific article

Abstract: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.
Keywords: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Published: 05.07.2017; Views: 358; Downloads: 39
.pdf Full text (182,69 KB)
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