scholarly journals Connectivity and some other properties of generalized Sierpiński graphs

2018 ◽  
Vol 12 (2) ◽  
pp. 401-412
Author(s):  
Sandi Klavzar ◽  
Sara Zemljic
Keyword(s):  
Positive Integer ◽  
Explicit Formula ◽  
Complete Graph ◽  
Building Block ◽  
Connected Components ◽  
Edge Connectivity ◽  
Sierpiński Graphs

If G is a graph and n a positive integer, then the generalized Sierpi?ski graph SnG is a fractal-like graph that uses G as a building block. The construction of SnG generalizes the classical Sierpi?ski graphs Sn p, where the role of G is played by the complete graph Kp. An explicit formula for the number of connected components in SnG is given and it is proved that the (edge-)connectivity of SnG equals the (edge-)connectivity of G. It is demonstrated that SnG contains a 1-factor if and only if G contains a 1-factor. Hamiltonicity of generalized Sierpi?ski graphs is also discussed.

AN EFFICIENT DISTRIBUTED ALGORITHM FOR 3-EDGE-CONNECTIVITY

2006 ◽  
Vol 17 (03) ◽  
pp. 677-701 ◽  
Author(s):  
YUNG H. TSIN
Keyword(s):  
Distributed Algorithm ◽  
Computer Network ◽  
Connected Components ◽  
Message Complexity ◽  
Edge Connectivity ◽  
Worst Case ◽  
Dense Networks

A distributed algorithm for finding the cut-edges and the 3-edge-connected components of an asynchronous computer network is presented. For a network with n nodes and m links, the algorithm has worst-case [Formula: see text] time and O(m + nhT) message complexity, where hT < n. The algorithm is message optimal when [Formula: see text] which includes dense networks (i.e. m ∈ Θ(n2)). The previously best known distributed algorithm has a worst-case O(n3) time and message complexity.

scholarly journals Graph connectivity and Wiener index

2006 ◽  
Vol 133 (31) ◽  
pp. 1-5 ◽  
Author(s):  
I. Gutman ◽  
S. Zhang
Keyword(s):  
Complete Graph ◽  
Wiener Index ◽  
Graph Connectivity ◽  
Subject Classification ◽  
Edge Connectivity

The graphs with a given number n of vertices and given (vertex or edge) connectivity k, having minimum Wiener index are determined. In both cases this is Kk + (K1 U Kn-k-1), the graph obtained by connecting all vertices of the complete graph Kk with all vertices of the graph whose two components are Kn-k-1 and K1. AMS Mathematics Subject Classification (2000): 05C12, 05C40 05C35.

Component Edge Connectivity of Hypercubes

2018 ◽  
Vol 29 (06) ◽  
pp. 995-1001 ◽  
Author(s):  
Shuli Zhao ◽  
Weihua Yang ◽  
Shurong Zhang ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Complete Graph ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Optimal Solutions ◽  
Edge Connectivity ◽  
Important Measure ◽  
Minimum Number ◽  
Text Component

Fault tolerance is an important issue in interconnection networks, and the traditional edge connectivity is an important measure to evaluate the robustness of an interconnection network. The component edge connectivity is a generalization of the traditional edge connectivity. The [Formula: see text]-component edge connectivity [Formula: see text] of a non-complete graph [Formula: see text] is the minimum number of edges whose deletion results in a graph with at least [Formula: see text] components. Let [Formula: see text] be an integer and [Formula: see text] be the decomposition of [Formula: see text] such that [Formula: see text] and [Formula: see text] for [Formula: see text]. In this note, we determine the [Formula: see text]-component edge connectivity of the hypercube [Formula: see text], [Formula: see text] for [Formula: see text]. Moreover, we classify the corresponding optimal solutions.

The Oslo Accords and Palestinian Civil Society

2017 ◽  
Author(s):  
Liv Tørres
Keyword(s):  
Civil Society ◽  
Building Block ◽  
Organizational Capacity ◽  
The State ◽  
Efficient Tool ◽  
Palestinian Territories ◽  
Oslo Accords ◽  
Israeli Occupation ◽  
Internal Division

This chapter discusses the role of civil society in helping Palestinians challenge Israeli occupation. Palestinian organizations have developed despite the absence of the state, independence, sovereignty, and citizenship. Organizational capacity and activism are an efficient tool and building block for unity and power here as elsewhere, which in turn will help Palestinians challenge their circumstances. The Norwegian People's Aid (NPA) has been active in the Occupied Palestinian Territories since 1987. Its goal is to help build the organizational and collective muscles of Palestinians to challenge occupation, oppression, and internal division. It is against this background that the NPA works in partnership with local Palestinian organizations. It is on this basis that they believe it is important to work with local forces rather than simply provide services. And it is from this perspective that they have watched the development of Palestinian civil society and the tensions, changes, and challenges that followed the Oslo Accords.

A study on distance in graph complement

2020 ◽  
Vol 12 (03) ◽  
pp. 2050045
Author(s):  
A. Chellaram Malaravan ◽  
A. Wilson Baskar
Keyword(s):  
Positive Integer ◽  
Complete Graph ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The aim of this paper is to determine radius and diameter of graph complements. We provide a necessary and sufficient condition for the complement of a graph to be connected, and determine the components of graph complement. Finally, we completely characterize the class of graphs [Formula: see text] for which the subgraph induced by central (respectively peripheral) vertices of its complement in [Formula: see text] is isomorphic to a complete graph [Formula: see text], for some positive integer [Formula: see text].

The Reaction Pathway of Cellulose Pyrolysis to a Multifunctional Chiral Building Block: The Role of Water Unveiled by a DFT Computational Investigation

ChemPhysChem ◽  
2016 ◽  
Vol 17 (23) ◽  
pp. 3948-3953 ◽  
Author(s):  
Tainah Dorina Marforio ◽  
Andrea Bottoni ◽  
Matteo Calvaresi ◽  
Daniele Fabbri ◽  
Pietro Giacinto ◽  
...  
Keyword(s):  
Building Block ◽  
Reaction Pathway ◽  
Computational Investigation ◽  
Cellulose Pyrolysis ◽  
Chiral Building Block

Engineering Nanoparticle Cluster Arrays for Bacterial Biosensing: The Role of the Building Block in Multiscale SERS Substrates

2010 ◽  
Vol 20 (16) ◽  
pp. 2619-2628 ◽  
Author(s):  
Linglu Yang ◽  
Bo Yan ◽  
W. Ranjith Premasiri ◽  
Lawrence D. Ziegler ◽  
Luca Dal Negro ◽  
...  
Keyword(s):  
Building Block ◽  
Sers Substrates ◽  
Nanoparticle Cluster

On the Structure of G(H, k)

2014 ◽  
Vol 21 (02) ◽  
pp. 317-330 ◽  
Author(s):  
Guixin Deng ◽  
Pingzhi Yuan
Keyword(s):  
Abelian Group ◽  
Positive Integer ◽  
Explicit Formula ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Directed Edge ◽  
Necessary And Sufficient

Let H be an abelian group written additively and k be a positive integer. Let G(H, k) denote the digraph whose set of vertices is just H, and there exists a directed edge from a vertex a to a vertex b if b = ka. In this paper we give a necessary and sufficient condition for G(H, k1) ≃ G(H, k2). We also discuss the problem when G(H1, k) is isomorphic to G(H2, k) for a given k. Moreover, we give an explicit formula of G(H, k) when H is a p-group and gcd (p, k)=1.

ON MODAL μ-CALCULUS OVER FINITE GRAPHS WITH SMALL COMPONENTS OR SMALL TREE WIDTH

2012 ◽  
Vol 23 (03) ◽  
pp. 627-647
Author(s):  
GIOVANNA D'AGOSTINO ◽  
GIACOMO LENZI
Keyword(s):  
Positive Integer ◽  
Upper Bounds ◽  
Connected Components ◽  
Small Tree ◽  
Strongly Connected Components ◽  
Finite Graphs ◽  
Strongly Connected ◽  
Tree Width ◽  
Parity Games ◽  
Alternating Automata

This paper is a continuation and correction of a paper presented by the same authors at the conference GANDALF 2010. We consider the Modal μ-calculus and some fragments of it. For every positive integer k we consider the class SCCk of all finite graphs whose strongly connected components have size at most k, and the class TWk of all finite graphs of tree width at most k. As upper bounds, we show that for every k, the temporal logic CTL* collapses to alternation free μ-calculus in SCCk; and in TW1, the winning condition for parity games of any index n belongs to the level Δ2 of Modal μ-calculus. As lower bounds, we show that Büchi automata are not closed under complement in TW2 and coBüchi nondeterministic and alternating automata differ in TW1.

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