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Modern Applications of Graph Theory (2019)
Book
Zverovich, V. (in press). Modern Applications of Graph Theory. Oxford, UK: Oxford University Press

This book discusses many modern, cutting-edge applications of graph theory, such as traffic networks, navigable networks and optimal routing for emergency response, placement of electric vehicle charging stations and graph-theoretic methods in comput... Read More about Modern Applications of Graph Theory.

The likelihood of Braess' paradox in traffic networks (2018)
Book Chapter
Zverovich, V. The likelihood of Braess' paradox in traffic networks. In Modern Applications of Graph TheoryManuscript submitted for publication

The well-known Braess' paradox illustrates situations when adding a new link to a traffic network might increase congestion in the network. In this article, we announce a number of new results devoted to the probability of Braess' paradox to occur in... Read More about The likelihood of Braess' paradox in traffic networks.

Extending indoor open street mapping environments to navigable 3D citygml building models: Emergency response assessment (2018)
Journal Article
Fadli, F., Kutty, N., Wang, Z., Zlatanova, S., Mahdjoubi, L., Boguslawski, P., & Zverovich, V. (2018). Extending indoor open street mapping environments to navigable 3D citygml building models: Emergency response assessment. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 42(4), 241-247. https://doi.org/10.5194...rchives-XLII-4-161-2018

© Authors 2018. Disaster scenarios in high-rise buildings such as the Address Downtown, Dubai or Grenfell Tower, London have showed ones again the importance of data information availability for emergency management in buildings. 3D visualization of... Read More about Extending indoor open street mapping environments to navigable 3D citygml building models: Emergency response assessment.

Analytic prioritization of indoor routes for search and rescue operations in hazardous environments (2017)
Journal Article
Zverovich, V., Mahdjoubi, L., Boguslawski, P., & Fadli, F. (2017). Analytic prioritization of indoor routes for search and rescue operations in hazardous environments. Computer-Aided Civil and Infrastructure Engineering, 32(9), 727-747. https://doi.org/10.1111/mice.12260

Applications to prioritize indoor routes for emergency situations in a complex built facility have been restricted to building simulations and network approaches. These types of applications often failed to account for the complexity and trade-offs... Read More about Analytic prioritization of indoor routes for search and rescue operations in hazardous environments.

Emergency response in complex buildings: Automated selection of safest and balanced routes (2016)
Journal Article
Zverovich, V., Mahdjoubi, L., Boguslawski, P., Fadli, F., & Barki, H. (2016). Emergency response in complex buildings: Automated selection of safest and balanced routes. Computer-Aided Civil and Infrastructure Engineering, 31(8), 617-632. https://doi.org/10.1111/mice.12197

The extreme importance of emergency response in complex buildings during natural and human-induced disasters has been widely acknowledged. In particular, there is a need for efficient algorithms for finding safest evacuation routes, which would take... Read More about Emergency response in complex buildings: Automated selection of safest and balanced routes.

On general frameworks and threshold functions for multiple domination (2015)
Journal Article
Zverovich, V. (2015). On general frameworks and threshold functions for multiple domination. Discrete Mathematics, 338(11), 2095-2104. https://doi.org/10.1016/j.disc.2015.05.003

© 2015 Elsevier B.V. All rights reserved. We consider two general frameworks for multiple domination, which are called (r,s)-domination and parametric domination. They generalise and unify {k}-domination, k-domination, total k-domination and k-tuple... Read More about On general frameworks and threshold functions for multiple domination.

Braess’ paradox in asymmetrical traffic networks (2014)
Presentation / Conference
Zverovich, V., & Avineri, E. (2014, January). Braess’ paradox in asymmetrical traffic networks. Poster presented at Transportation Research Board Conference

Braess’ paradox illustrates situations when adding a new link to a transport network might lead to an equilibrium state in which travel times of users will increase. Braess’ paradox has been studied mainly in the context of the classical problem intr... Read More about Braess’ paradox in asymmetrical traffic networks.

Upper bounds for the bondage number of graphs on topological surfaces (2013)
Journal Article
Gagarin, A., & Zverovich, V. (2013). Upper bounds for the bondage number of graphs on topological surfaces. Discrete Mathematics, 313(11), 1132-1137. https://doi.org/10.1016/j.disc.2011.10.018

The bondage number b(G) of a graph G is the smallest number of edges of G whose removal results in a graph having the domination number larger than that of G. We show that, for a graph G having the maximum vertex degree Δ(G) and embeddable on an orie... Read More about Upper bounds for the bondage number of graphs on topological surfaces.

Discrepancy and signed domination in graphs and hypergraphs (2010)
Journal Article
Zverovich, V., Poghosyan, A., Poghosyan, A., & Zverovich, V. (2010). Discrepancy and signed domination in graphs and hypergraphs. Discrete Mathematics, 310(15-16), 2091-2099. https://doi.org/10.1016/j.disc.2010.03.030

For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and -1 such that the closed neighbourhood of every vertex contains more +1's than -1's. This concept is closely related to combinatorial discrepa... Read More about Discrepancy and signed domination in graphs and hypergraphs.

Upper bounds for α-domination parameters (2009)
Journal Article
Gagarin, A., Poghosyan, A., & Zverovich, V. (2009). Upper bounds for α-domination parameters. Graphs and Combinatorics, 25(4), 513-520. https://doi.org/10.1007/s00373-009-0864-6

We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic constructi... Read More about Upper bounds for α-domination parameters.

The k-tuple domination number revisited (2008)
Journal Article
Zverovich, V. (2008). The k-tuple domination number revisited. Applied Mathematics Letters, 21(10), 1005-1011. https://doi.org/10.1016/j.aml.2007.10.016

The following fundamental result for the domination number γ (G) of a graph G was proved by Alon and Spencer, Arnautov, Lovász and Payan: γ (G) ≤ frac(ln (δ + 1) + 1, δ + 1) n, where n is the order and δ is the minimum degree of vertices of G. A simi... Read More about The k-tuple domination number revisited.

A generalised upper bound for the k-tuple domination number (2008)
Journal Article
Zverovich, V. E., Gagarin, A., & Zverovich, V. (2008). A generalised upper bound for the k-tuple domination number. Discrete Mathematics, 308(5-6), 880-885. https://doi.org/10.1016/j.disc.2007.07.033

In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G,γ× k (G) ≤ frac(ln (δ - k + 2) + ln (∑m = 1k - 1 (k - m) over(d... Read More about A generalised upper bound for the k-tuple domination number.


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