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引用次数: 0
摘要
摘要:给定图G = (V, E)，对一个顶点划分，我们关联一个矩阵𝒫-matrix，并定义𝒫-energy, E (G)为G的𝒫-matrix的𝒫-eigenvalues的和。除了研究𝒫-matrix的一些性质，它的特征值和𝒫-energy的界外，我们还探讨了图族中𝒫-energy的最大(最小)值的鲁棒性(剪切性)𝒫-energy。进一步，我们导出了几种不同顶点划分的图的显式公式E - p (G)。
Abstract Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.
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