Eigenfunctions of the Edge-Based Laplacian on a Graph
نویسندگان
چکیده
In this paper, we analyze the eigenfunctions of the edge-based Laplacian on a graph and the relationship of these functions to random walks on the graph. We commence by discussing the set of eigenfunctions supported at the vertices, and demonstrate the relationship of these eigenfunctions to the classical random walk on the graph. Then, from an analysis of functions supported only on the interior of edges, we develop a method for explicitly calculating the edge-interior eigenfunctions of the edge-based Laplacian. This reveals a connection between the edge-based Laplacian and the adjacency matrix of backtrackless random walk on the graph. The edge-based eigenfunctions therefore correspond to some eigenfunctions of the normalised Hashimoto matrix.
منابع مشابه
On net-Laplacian Energy of Signed Graphs
A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...
متن کاملThe Laplacian Polynomial and Kirchhoff Index of the k-th Semi Total Point Graphs
The k-th semi total point graph of a graph G, , is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of edge considered. In this paper, a formula for Laplacian polynomial of in terms of characteristic and Laplacian polynomials of G is computed, where is a connected regular graph.The Kirchhoff index of is also computed.
متن کاملEdge-based operators for graph characterization
This thesis addresses problems in computer vision and pattern recognition using graphs. The particular focus is on graph matching and characterization using edge-based operators. The thesis commences with a brief introduction in Chapter 1, followed by a review of the relevant literature in Chapter 2. The remainder of the thesis is organized as follows. Chapter 3 discusses the structure of the I...
متن کاملLaplacian Energy of a Fuzzy Graph
A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...
متن کاملOn Eccentricity Version of Laplacian Energy of a Graph
The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1302.3433 شماره
صفحات -
تاریخ انتشار 2013