Results 21 to 30 of about 3,180,841 (100)
On maximum degree (signless) Laplacian matrix of a graph
, 2022 Let G be a simple graph on n vertices and v1, v2, . . . , vn be the vertices ofG. We denote the degree of a vertex vi in G by dG(vi) = di. The maximumdegree matrix of G, denoted by M(G), is the real symmetric matrix withits ijth entry equal to max{di, dj}
Raghu, V. D. +2 more
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On the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph [PDF]
, 2013 summary:The Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph are the characteristic polynomials of its Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix, respectively.
Li, Jianxi, Guo, Ji-Ming, Shiu, Wai Chee
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, 2018 The distance signless Laplacian spectral radius of a connected graph [Formula: see text] is the largest eigenvalue of the distance signless Laplacian matrix of [Formula: see text], defined as [Formula: see text], where [Formula: see text] is the distance
Abdollah Alhevaz +2 more
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Resistance Distance and Kirchhoff Index for a Class of Graphs
Mathematical Problems in Engineering, Volume 2018, Issue 1, 2018., 2018 Let G[F, Vk, Hv] be the graph with k pockets, where F is a simple graph of order n ≥ 1, Vk = {v1, v2, …, vk} is a subset of the vertex set of F, Hv is a simple graph of order m ≥ 2, and v is a specified vertex of Hv. Also let G[F, Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek = {e1, e2, …ek} is a subset of the ...
WanJun Yin +3 more
wiley +1 more source
Bipartite subgraphs and the signless Laplacian matrix [PDF]
, 2011 For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue.
Debdas Paul, Steve Kirkland
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On the signless Laplacian and normalized signless Laplacian spreads of graphs
, 2022 Let G = (V, E), V = {v1, v2, …, vn}, be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≽ d2 ≽ … ≽ dn. Denote by A and D the adjacency matrix and diagonal vertex degree matrix of G, respectively.
Igor Milovanović +8 more
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Generalized Characteristic Polynomials of Join Graphs and Their Applications
Discrete Dynamics in Nature and Society, Volume 2017, Issue 1, 2017., 2017 The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices of G in electrical networks. LEL(G) is the Laplacian‐Energy‐Like Invariant of G in chemistry. In this paper, we define two classes of join graphs: the subdivision‐vertex‐vertex join G1⊚G2 and the subdivision‐edge‐edge join G1⊝G2.
Pengli Lu +3 more
wiley +1 more source
The signless Laplacian matrix of hypergraphs [PDF]
, 2022 In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph ...
Cardoso, Kauê da Rosa, Trevisan, Vilmar
core
Bounds on the Spectral Radius of a Nonnegative Matrix and Its Applications
Journal of Applied Mathematics, Volume 2016, Issue 1, 2016., 2016 We obtain the sharp bounds for the spectral radius of a nonnegative matrix and then obtain some known results or new results by applying these bounds to a graph or a digraph and revise and improve two known results.
Danping Huang, Lihua You, Ali R. Ashrafi
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Spectral Characterizations of the Aα−‐Matrix for Graph Products
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.For α ∈ [0, 1], the matrix Aα−G=αDG+α−1AG defines a Laplacian–type operator associated with a graph G, interpolating between −A(G) and D(G). In this paper, we develop a systematic study of the Aα−‐spectrum under several classical graph products.
Zakeiah Alkhamisi +4 more
wiley +1 more source