isoperimetric number
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Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 452
Author(s):  
Yilun Shang

Social networks describe social interactions between people, which are often modeled by intersection graphs. In this paper, we propose an intersection graph model that is induced by adding a sparse random bipartite graph to a given bipartite graph. Under some mild conditions, we show that the vertex–isoperimetric number and the edge–isoperimetric number of the randomly perturbed intersection graph on n vertices are Ω ( 1 / ln n ) asymptomatically almost surely. Numerical simulations for small graphs extracted from two real-world social networks, namely, the board interlocking network and the scientific collaboration network, were performed. It was revealed that the effect of increasing isoperimetric numbers (i.e., expansion properties) on randomly perturbed intersection graphs is presumably independent of the order of the network.


10.37236/7410 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Changjiang Bu ◽  
Haifeng Li ◽  
Jiang Zhou

In this paper, we show that a uniform hypergraph $\mathcal{G}$ is connected if and only if one of its inverse Perron values is larger than $0$. We give some bounds on the bipartition width, isoperimetric number and eccentricities of $\mathcal{G}$ in terms of inverse Perron values. By using the inverse Perron values, we give an estimation of the edge connectivity of a $2$-design, and determine the explicit edge connectivity of a symmetric design. Moreover, relations between the inverse Perron values and resistance distance of a connected graph are presented.  


10.37236/6980 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Andrew Elvey Price ◽  
Muhammad Adib Surani ◽  
Sanming Zhou

Let $\Gamma_{n,q}$ be the point-hyperplane incidence graph of the projective space $\operatorname{PG}(n,q)$, where $n \ge 2$ is an integer and $q$ a prime power. We determine the order of magnitude of $1-i_V(\Gamma_{n,q})$, where $i_V(\Gamma_{n,q})$ is the vertex-isoperimetric number of $\Gamma_{n,q}$. We also obtain the exact values of $i_V(\Gamma_{2,q})$ and the related incidence-free number of $\Gamma_{2,q}$ for $q \le 16$.


2018 ◽  
Vol 87 (5) ◽  
pp. 957-970
Author(s):  
Alice M. W. Hui ◽  
Muhammad Adib Surani ◽  
Sanming Zhou
Keyword(s):  

2018 ◽  
Vol 34 ◽  
pp. 428-443 ◽  
Author(s):  
Aida Abiad ◽  
Boris Brimkov ◽  
Xavier Martinez-Rivera ◽  
Suil O ◽  
Jingmei Zhang

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar.


2013 ◽  
Vol 46 (12) ◽  
pp. 3371-3382 ◽  
Author(s):  
A. Daneshgar ◽  
R. Javadi ◽  
S.B. Shariat Razavi

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ersin Aslan ◽  
Alpay Kirlangic

The isoperimetric number of a graph , denoted by , was introduced by Mohar (1987). A graph and a subset of its vertices are given, and let denote the edge boundary of , the set of edges which connects vertices in to vertices not in . The isoperimetric number of is defined as . In this paper, some results about the isoperimetric number of graphs obtained by graph operations are given.


2009 ◽  
Vol 22 (9) ◽  
pp. 1451-1457
Author(s):  
Zhantao Huang ◽  
Yinglie Jin ◽  
Ke Liang

2004 ◽  
Vol 138 (1-2) ◽  
pp. 3-12 ◽  
Author(s):  
M Cemil Azizoğlu ◽  
Ömer Eğecioğlu

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