Hypergraph products for structural mechanics |
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| Affiliation: | 1. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, P.O. Box 16846-13114, Tehran, Iran;2. Department of Engineering, University of Maragheh, Maragheh, Iran;1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, PR China;2. School of Mathematical Sciences, Harbin Normal University, Harbin 150025, PR China;1. Department of Civil Engineering, Maragheh Branch, Islamic Azad University, Maragheh, Iran;2. Department of Civil Engineering, Maragheh University, Maragheh, Iran |
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| Abstract: | In this paper Cartesian, direct and strong Cartesian product of hypergraphs are investigated. A new concept named the adjacency function is defined on hypergraphs. This definition leads to distinct adjacency and Laplacian matrices for a hypergraph and makes it possible to express it in an algebraic form. Variable adjacency functions on hypergraphs result in generation of dynamic graph products which are applied to dynamic systems. For further clarity, some examples from structural mechanics are provided. The generality of the approach is shown through some examples, indicating this fact that the hypergraph products can encompass most of the available developments on the graph products in the literature. |
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| Keywords: | Hypergraph products Dynamic graph products Variable adjacency function Configuration processing Adjacency matrix Laplacian matrix |
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