Number of spanning trees of some families of graphs generated by a triangle

Daoud, S. N.

doi:10.1080/16583655.2019.1626074

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…2) where G-e denotes the graph obtained by deleting an arbitrary edge e, and G/e denotes the graph obtained by contracting an arbitrary edge e [1,9]. For more results, see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In this paper we contribute a new algebraic method which is based on Dodgson and Chio's method.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2023

J GRAPH-HOC

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The complexity of a graph can be determined using a network-theoretic method, which is given. This strategy is based on the connection between graph theory and the theory of determinants in linear algebra. In this article, we provide a unique algebraic method that makes use of linear algebra to derive simple formulas for the complexity of diverse novel networks. We can derive the explicit formulas for the globe network and its subdivision using this method. In the final least, we also determine their spanning trees entropy and compare it to each other.

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Section: Introductionmentioning

confidence: 99%

Untitled

2023

J GRAPH-HOC

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“…The prism n R is defined as the graph obtained by adding to these two cycles all the edges of the form i i. vw . The number of spanning trees in more results, it is suggested to see these articles[15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

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confidence: 99%

Complexity of Some Types of Cyclic Snake Graphs

Mohamed,

Amin

2024

MMA

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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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Number of spanning trees of some families of graphs generated by a triangle

Cited by 2 publications

References 19 publications

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Complexity of Some Types of Cyclic Snake Graphs

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