Mathematical Modelling and Applications

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Complexity of Some Types of Cyclic Snake Graphs

Received: 5 December 2023    Accepted: 26 December 2023    Published: 20 February 2024
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Abstract

The number of spanning trees in graphs (networks) is a crucial invariant, and it is also an important measure of the reliability of a network. Spanning trees are special subgraphs of a graph that have several important properties. First, T must span G, which means it must contain every vertex in graph G, if T is a spanning tree of graph G. T needs to be a subgraph of G, second. Stated differently, any edge present in T needs to be present in G as well. Third, G is the same as T if each edge in T is likewise present in G. In path-finding algorithms like Dijkstra's shortest path algorithm and A* search algorithm, spanning trees play an essential part. In those approaches, spanning trees are computed as component components. Protocols for network routing also take advantage of it. In numerous techniques and applications, minimum spanning trees are highly beneficial. Computer networks, electrical grids, and water networks all frequently use them. They are also utilized in significant algorithms like the min-cut max-flow algorithm and in graph issues like the travelling salesperson problem. In this paper, we use matrix analysis and linear algebra techniques to obtain simple formulas for the number of spanning trees of certain kinds of cyclic snake graphs.

DOI 10.11648/j.mma.20240901.12
Published in Mathematical Modelling and Applications (Volume 9, Issue 1, March 2024)
Page(s) 14-22
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Cyclic Snakes, Subdivision, Edge Contraction, Spanning Trees

References
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[3] Petingi, L., Boesch, F., & Suffel, C. (1998). On the characterization of graphs with maximum number of spanning trees. Discrete mathematics, 179(1-3), 155-166.
[4] Brown, T. J., Mallion, R. B., Pollak, P., & Roth, A. (1996). Some methods for counting the spanning trees in labelled molecular graphs, examined in relation to certain fullerenes. Discrete Applied Mathematics, 67(1-3), 51-66.
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[11] Sedlacek, J. (1970). On the skeletons of a graph or digraph. In Proc. Calgary International Conference on Combinatorial Structures and their Applications, Gordon and Breach (pp. 387-391).
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[22] B. Mohamed, L. Mohaisen and M. Amin, Binary Equilibrium Optimization Algorithm for Computing Connected Domination Metric Dimension Problem, Sci. Program, 2022.
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  • APA Style

    Mohamed, B., Amin, M. (2024). Complexity of Some Types of Cyclic Snake Graphs. Mathematical Modelling and Applications, 9(1), 14-22. https://doi.org/10.11648/j.mma.20240901.12

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    ACS Style

    Mohamed, B.; Amin, M. Complexity of Some Types of Cyclic Snake Graphs. Math. Model. Appl. 2024, 9(1), 14-22. doi: 10.11648/j.mma.20240901.12

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    AMA Style

    Mohamed B, Amin M. Complexity of Some Types of Cyclic Snake Graphs. Math Model Appl. 2024;9(1):14-22. doi: 10.11648/j.mma.20240901.12

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  • @article{10.11648/j.mma.20240901.12,
      author = {Basma Mohamed and Mohamed Amin},
      title = {Complexity of Some Types of Cyclic Snake Graphs},
      journal = {Mathematical Modelling and Applications},
      volume = {9},
      number = {1},
      pages = {14-22},
      doi = {10.11648/j.mma.20240901.12},
      url = {https://doi.org/10.11648/j.mma.20240901.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20240901.12},
      abstract = {The number of spanning trees in graphs (networks) is a crucial invariant, and it is also an important measure of the reliability of a network. Spanning trees are special subgraphs of a graph that have several important properties. First, T must span G, which means it must contain every vertex in graph G, if T is a spanning tree of graph G. T needs to be a subgraph of G, second. Stated differently, any edge present in T needs to be present in G as well. Third, G is the same as T if each edge in T is likewise present in G. In path-finding algorithms like Dijkstra's shortest path algorithm and A* search algorithm, spanning trees play an essential part. In those approaches, spanning trees are computed as component components. Protocols for network routing also take advantage of it. In numerous techniques and applications, minimum spanning trees are highly beneficial. Computer networks, electrical grids, and water networks all frequently use them. They are also utilized in significant algorithms like the min-cut max-flow algorithm and in graph issues like the travelling salesperson problem. In this paper, we use matrix analysis and linear algebra techniques to obtain simple formulas for the number of spanning trees of certain kinds of cyclic snake graphs.
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     year = {2024}
    }
    

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    AB  - The number of spanning trees in graphs (networks) is a crucial invariant, and it is also an important measure of the reliability of a network. Spanning trees are special subgraphs of a graph that have several important properties. First, T must span G, which means it must contain every vertex in graph G, if T is a spanning tree of graph G. T needs to be a subgraph of G, second. Stated differently, any edge present in T needs to be present in G as well. Third, G is the same as T if each edge in T is likewise present in G. In path-finding algorithms like Dijkstra's shortest path algorithm and A* search algorithm, spanning trees play an essential part. In those approaches, spanning trees are computed as component components. Protocols for network routing also take advantage of it. In numerous techniques and applications, minimum spanning trees are highly beneficial. Computer networks, electrical grids, and water networks all frequently use them. They are also utilized in significant algorithms like the min-cut max-flow algorithm and in graph issues like the travelling salesperson problem. In this paper, we use matrix analysis and linear algebra techniques to obtain simple formulas for the number of spanning trees of certain kinds of cyclic snake graphs.
    
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Author Information
  • Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin Elkom, Egypt

  • Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin Elkom, Egypt

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