Laplacian eigenvalues and partition problems in hypergraphs
نویسنده
چکیده
We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on partition problems in hypergraphs which are computationally difficult to solve (NP-hard or NP-complete). Therefore it is very important to obtain nontrivial bounds. More precisely, the following parameters are bounded in the paper: bipartition width, averaged minimal cut, isoperimetric number, max-cut, independence number and domination number.
منابع مشابه
The clique and coclique numbers’ bounds based on the H-eigenvalues of uniform hypergraphs
In this paper, some inequality relations between the Laplacian/signless Laplacian H-eigenvalues and the clique/coclique numbers of uniform hypergraphs are presented. For a connected uniform hypergraph, some tight lower bounds on the largest Laplacian H+-eigenvalue and signless Laplacian H-eigenvalue related to the clique/coclique numbers are given. And some upper and lower bounds on the clique/...
متن کاملGeneralized Laplacian Eigenvalues of Random Hypergraphs
This is a sequel to an accepted talk of WAW 2011, where we introduced a set of generalized Laplacians of hypergraphs through the high-ordered random walks. In that paper, we proved the eigenvalues of these Laplacians can effectively control the mixing rate of highordered random walks, the generalized distances/diameters, and the edge expansions. In this talk, we will give a preliminary report o...
متن کاملEla Spectral Properties of Oriented Hypergraphs
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...
متن کاملAlgebraic Connectivity of Finite-element Hypergraphs
This paper generalizes results that relate the connectivity of a weighted graph to the smallest nonzero eigenvalue of the graph’s Laplacian matrix. We generalize these results to hypergraphs with vector-valued vertices and matrix-valued edges. Our definitions of hypergraphs and their connectivity are designed to model finite-element meshes. The physical interpretation of our results is as follo...
متن کاملSeidel Signless Laplacian Energy of Graphs
Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Appl. Math. Lett.
دوره 22 شماره
صفحات -
تاریخ انتشار 2009