Some bounds for total communicability of graphs
| Autor: | Kinkar Ch. Das, Ali Iranmanesh, Mohammad Ali Hosseinzadeh, Samaneh Hossein-Zadeh |
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| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Degree (graph theory) Spectral radius 010102 general mathematics 010103 numerical & computational mathematics Cartesian product 01 natural sciences Combinatorics symbols.namesake Tensor product Matrix function Product (mathematics) symbols Discrete Mathematics and Combinatorics Regular graph Geometry and Topology Adjacency matrix 0101 mathematics Mathematics |
| Zdroj: | Linear Algebra and its Applications. 569:266-284 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2019.01.023 |
| Popis: | In a network or a graph, the total communicability (TC) has been defined as the sum of the entries in the exponential of the adjacency matrix of the network. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable properties. In this paper, we obtain some bounds for total communicability of a graph G, T C ( G ) , in terms of spectral radius of the adjacency matrix, number of vertices, number of edges, minimum degree and the maximum degree of G. Moreover, we find some upper bounds for T C ( G ) when G is the Cartesian product, tensor product or the strong product of two graphs. In addition, Nordhaus–Gaddum-type results for the total communicability of a graph G are established. |
| Databáze: | OpenAIRE |
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