Complexity of Some Duplicating Networks
| Autor: | Walaa A. Aboamer, Mohamed R. Zeen El Deen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Computer Science
Diagonal splitting graph Complete bipartite graph Combinatorics ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION recurrence relation Symmetric matrix General Materials Science Computer Science::Symbolic Computation orthogonal polynomials ComputingMethodologies_COMPUTERGRAPHICS Mathematics Spanning tree General Engineering Complete graph Complexity shadow graph TK1-9971 TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Orthogonal polynomials Path (graph theory) Linear algebra ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::Programming Languages Electrical engineering. Electronics. Nuclear engineering MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | IEEE Access, Vol 9, Pp 56736-56756 (2021) |
| ISSN: | 2169-3536 |
| Popis: | There are plentiful ways to duplicate a graph (network), such as splitting, shadow, mirror, and total graph. In this paper, we derive an evident formula of the complexity, a number of spanning trees, of the closed helm graph, the mirror graph of the path and cycle, the total graph of the path, the cycle, and the wheel. Furthermore, we got an explicit formula for the splitting of a special family of graphs such as path, cycle, complete graph $K_{n}$ , complete bipartite graph $K_{n,n}$ , prism, diagonal prism, and the graphs obtained from the wheel and double wheel by splitting the vertices on their rim. Finally, an obvious formula for the complexity of $k-$ shadow graph for some graphs such as the path, the cycle, the wheel, the complete graph, and the fan graph $F_{n}$ has been obtained. These formulas have been discovered by employing techniques from linear algebra, orthogonal polynomials, and matrix theory. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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