The communicability distance in graphs
نویسنده
چکیده
Article history: Received 12 January 2012 Accepted 24 January 2012 Available online 25 February 2012 Submitted by R. Brualdi AMS classification: 05C12 05C50 15A18 15A16
منابع مشابه
Hyperspherical embedding of graphs and networks in communicability spaces
Let G be a simple connected graph with n nodes and let fαk (A) be a communicability function of the adjacency matrix A, which is expressible by the following Taylor series expansion: ∞ k=0 αkA k. We prove here that if fαk (A) is positive semidefinite then the function ηp,q = (fαk (A)pp+ fαk (A)qq−2fαk (A)pq) 1 2 is a Euclidean distance between the corresponding nodes of the graph. Then, we pr...
متن کاملComplex networks in the Euclidean space of communicability distances.
We study the properties of complex networks embedded in a Euclidean space of communicability distances. The communicability distance between two nodes is defined as the difference between the weighted sum of walks self-returning to the nodes and the weighted sum of walks going from one node to the other. We give some indications that the communicability distance identifies the least crowded rou...
متن کاملRemarks on Distance-Balanced Graphs
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.
متن کاملProduct version of reciprocal degree distance of composite graphs
A {it topological index} of a graph is a real number related to the graph; it does not depend on labeling or pictorial representation of a graph. In this paper, we present the upper bounds for the product version of reciprocal degree distance of the tensor product, join and strong product of two graphs in terms of other graph invariants including the Harary index and Zagreb indices.
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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 2012