The Complexity of Wheel Graphs with Multiple Edges and Vertices

Wei, Yongzhuang; Gao, Zhicheng; Lu, Xiaoyun

doi:10.9734/arjom/2023/v19i9694

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Literature Review Of Studies Of Wheel Graphs1

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2023

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“…In 2022, Kuswardi et al [21] investigated the chromatic number of the amalgamation of wheel graphs. In June 2023, Wei et al [22] studied the complexity of wheel graphs with multiple edges and vertices. In July 2023, Greeni et al [23] explained the embedding of a complete bipartite graph into a wheel-related graph.…”

Section: Literature Review Of Studies Of Wheel Graphsmentioning

confidence: 99%

On Laplacian Eigenvalues of Wheel Graphs

Alotaibi,

Alghamdi,

Alolaiyan

2023

Symmetry

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Consider G to be a simple graph with n vertices and m edges, and L(G) to be a Laplacian matrix with Laplacian eigenvalues of μ1,μ2,…,μn=zero. Write Sk(G)=∑i=1kμi as the sum of the k-largest Laplacian eigenvalues of G, where k∈{1,2,…,n}. The motivation of this study is to solve a conjecture in algebraic graph theory for a special type of graph called a wheel graph. Brouwer’s conjecture states that Sk(G)≤m+k+12, where k=1,2,…,n. This paper proves Brouwer’s conjecture for wheel graphs. It also provides an upper bound for the sum of the largest Laplacian eigenvalues for the wheel graph Wn+1, which provides a better approximation for this upper bound using Brouwer’s conjecture and the Grone–Merris–Bai inequality. We study the symmetry of wheel graphs and recall an example of the symmetry group of Wn+1, n≥3. We obtain our results using majorization methods and illustrate our findings in tables, diagrams, and curves.

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Section: Literature Review Of Studies Of Wheel Graphsmentioning

confidence: 99%