My Favorite Application Using Graph Eigenvalues: Graph Energy
نویسنده
چکیده
The energy of a graph G, often denoted E(G), is defined to be the sum of the absolute value of the eigenvalues of its adjacency matrix. This graph invariant is very closely connected to a chemical quantity known as the total π-electron energy of conjugated hydrocarbon molecules. Very recently graph energy has become a quantity of interest to mathematicians, and several variations have been introduced. Here we present some of the history, basic definitions, and proof techniques used to study energy. We also list a few basic results of the field.
منابع مشابه
My favorite application using eigenvalues
In 2003 Vladimir Nikiforov [7] began a line of research whose aim was to build an extremal theory of graphs based on spectral theory. We will discuss some of his results and in particular we will focus on a result of Babai and Guiduli [1] that gives a Kövari-Sós-Turán type upper bound on the largest eigenvalue of the adjacency matrix of a Ks,t-free graph. This spectral approach sheds new light ...
متن کاملMy favorite application using eigenvalues: Eigenvalues and the Graham-Pollak Theorem
The famous Graham-Pollak Theorem states that one needs at least n− 1 complete bipartite subgraphs to partition the edge set of the complete graph on n vertices. Originally proved in conjunction with addressing for networking problems, this theorem is also related to perfect hashing and various questions about communication complexity. Since it’s original proof using Sylvester’s Law of Intertia,...
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 کاملLaplacian Sum-Eccentricity Energy of a Graph
We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...
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:
دوره شماره
صفحات -
تاریخ انتشار 2013