Applications of a theorem by Ky Fan in the theory of weighted Laplacian graph energy

Ataei, Alireza; Panahbar, Habibeh; Sharafdini, Reza

doi:10.20852/ntmsci.2017.207

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Md(x) ≤ Var(x)1

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“…, µ n be eigenvalues of the weighted Laplacian matrix L ω (G) of graph G with respect to the vertex weight ω. Then we [26] proposed the Laplacian energy LE ω (G) of G with respect to the vertex weight ω as…”

Section: Md(x) ≤ Var(x)mentioning

confidence: 99%

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Vertex weighted Laplacian graph energy and other topological indices

Sharafdini¹,

Panahbar²

2016

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Let G be a graph with a vertex weight ω and the vertices v 1 , . . . , v n . The Laplacian matrix of G with respect to ω is defined asThen the Laplacian energy of G with respect to ω defined asIn this paper we consider several natural vertex weights of G and obtain some inequalities between the ordinary and Laplacian energies of G with corresponding vertex weights. Finally, we apply our results to the molecular graph of toroidal fullerenes (or achiral polyhex nanotorus).

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Section: Md(x) ≤ Var(x)mentioning

confidence: 99%

“…Then the matrices L deg (G) = D deg (G) − A(G) and L † deg (G) = A(G) + D deg (G) are called Laplacian and signless Laplacian matrix of G, respectively (see [8], [9], [19], [20], [21] and [22]). These matrices was generalized for arbitrary vertex weighted graphs (see [26] and [27]). Let G be a simple graph with the vertex weight ω.…”

Section: Introductionmentioning

confidence: 99%