[HTML][HTML] Algorithm for recognizing Cartesian graph bundles

B Zmazek, J Žerovnik - Discrete applied mathematics, 2002 - Elsevier
Graph bundles generalize the notion of covering graphs and graph products. In, authors
constructed an algorithm that finds a presentation as a nontrivial Cartesian graph bundle for …

Graph bundles and Ricci‐flatness

W Li, S Liu - Bulletin of the London Mathematical Society, 2024 - Wiley Online Library
We develop a systematic way of constructing S‐Ricci flat graphs that are not Abelian Cayley
via graph bundle with explicit examples. For this purpose, we prove that, with some natural …

[HTML][HTML] The edge fault-diameter of Cartesian graph bundles

I Banič, R Erveš, J Žerovnik - European Journal of Combinatorics, 2009 - Elsevier
A Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph
product. Let G be a kG-edge connected graph and D̄c (G) be the largest diameter of …

[HTML][HTML] Mixed fault diameter of Cartesian graph bundles

R Erveš, J Žerovnik - Discrete applied mathematics, 2013 - Elsevier
The mixed fault diameter D (p, q)(G) is the maximum diameter among all subgraphs
obtained from graph G by deleting p vertices and q edges. A graph is (p, q)+ connected if it …

On domination numbers of graph bundles

B Zmazek, J Zerovnik - Journal of Applied Mathematics and Computing, 2006 - Springer
Let γ (G) be the domination number of a graph G. It is shown that for any κ≥ 0 there exists a
Cartesian graph bundle B█ φF such that γ (B█ φF)= γ (B) γ (F)—2 κ. The domination …

[PDF][PDF] Recognizing weighted directed Cartesian graph bundles

B Zmazek, J Zerovnik - Discussiones Mathematicae Graph …, 2000 - bibliotekanauki.pl
In this paper we show that methods for recognizing Cartesian graph bundles can be
generalized to weighted digraphs. The main result is an algorithm which lists the sets of …

Mixed connectivity of Cartesian graph products and bundles

R Erves, J Zerovnik - arXiv preprint arXiv:1002.2508, 2010 - arxiv.org
Mixed connectivity is a generalization of vertex and edge connectivity. A graph is $(p, 0) $-
connected, $ p> 0$, if the graph remains connected after removal of any $ p-1$ vertices. A …

[HTML][HTML] Improved upper bounds for vertex and edge fault diameters of Cartesian graph bundles

R Erveš, J Žerovnik - Discrete Applied Mathematics, 2015 - Elsevier
Mixed fault diameter of a graph G, D (a, b)(G), is the maximal diameter of G after deletion of
any a vertices and any b edges. Special cases are the (vertex) fault diameter D a V= D (a, 0) …

[HTML][HTML] Unique square property, equitable partitions, and product-like graphs

M Hellmuth, L Ostermeier, PF Stadler - Discrete Mathematics, 2014 - Elsevier
Equivalence relations on the edge set of a graph G that satisfy restrictive conditions on
chordless squares play a crucial role in the theory of Cartesian graph products and graph …

[PDF][PDF] On vulnerability measures of networks

R Erveš, D Rupnik Poklukar, J Žerovnik - … operational research review, 2013 - hrcak.srce.hr
ON VULNERABILITY MEASURES OF NETWORKS Page 1 Croatian Operational Research
Review (CRORR), Vol. 4, 2013 318 ON VULNERABILITY MEASURES OF NETWORKS 1 Rija …