On the minimum number of edges of two-connected graphs with given diameter

Jarry, Aubin; Laugier, Alexandre

doi:10.1016/j.disc.2011.11.017

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…the obtained d ij values define the availability matrix (D) and contribute to the identification of the minimum network with total connectivity at maximum availability that joins all nodes without redundancies. For undirected connected graphs, this network consists of n-1 arcs, where n is the number of nodes [42] with the highest availability values. The best-performing arcs should connect all the identified strategic buildings and road intersections, ensuring the most available acyclic path between them without redundances.…”

Section: Methodsmentioning

confidence: 99%

Consistency of Urban Roads to Manage Emergencies: Methodology to Identify the Minimum Network with Total Connectivity at Maximum Availability

Galiano

Moretti

2021

Sustainability

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Natural disasters happen without warning; it is normally impossible to predict when they will occur, but it is necessary that rescue services reach the disaster site and manage the emergency. This paper proposes an innovative methodology to summarize seismic effects on road, building, and land factors in urban areas. The existing road network is modelled through the graph theory: the arcs represent the main infrastructures, while the nodes represent both the primary strategic buildings and the intersections between the main roads. Therefore, the quantitative approach takes into account the existing road network, the focal areas that play a strategic role during emergency, and their relationship with buildings and territory. The results enable the identification of the minimum urban structure (MUS) with total connectivity at maximum availability. These structures were composed of the paths that will be the priority choice for emergency vehicles after an earthquake. The proposed approach has been implemented to identify the MUS in a medium-size Italian urban center (Pomezia) in the event of a critical earthquake. The methodology is easy to apply and could represent an ideal tool in the preliminary phase of analysis of an urban road network to define new city plans through targeted territorial design, to facilitate decision makers in investment choices, to increase the road network consistency, and to implement emergency plans after natural disasters.

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Section: Methodsmentioning

confidence: 99%

Consistency of Urban Roads to Manage Emergencies: Methodology to Identify the Minimum Network with Total Connectivity at Maximum Availability

Galiano

Moretti

2021

Sustainability

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Note on Minimally d-Rainbow Connected Graphs

Sun

et al. 2013

Graphs and Combinatorics

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An edge-colored graph G, where adjacent edges may have the same color, is rainbow connected if every two vertices of G are connected by a path whose edge has distinct colors. A graph G is k-rainbow connected if one can use k colors to make G rainbow connected. For integers n and d let t(n, d) denote the minimum size (number of edges) in k-rainbow connected graphs of order n. Schiermeyer got some exact values and upper bounds for t(n, d). However, he did not get a lower bound of t(n, d) for 3 ≤ d < ⌈ n 2 ⌉. In this paper, we improve his lower bound of t(n, 2), and get a lower bound of t(n, d) for 3 ≤ d < ⌈ n 2 ⌉.

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On the minimum number of edges of two-connected graphs with given diameter

Cited by 2 publications

References 8 publications

Consistency of Urban Roads to Manage Emergencies: Methodology to Identify the Minimum Network with Total Connectivity at Maximum Availability

Consistency of Urban Roads to Manage Emergencies: Methodology to Identify the Minimum Network with Total Connectivity at Maximum Availability

Note on Minimally d-Rainbow Connected Graphs

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