Results 21 to 30 of about 2,420 (96)
Degree Sum Condition for the Existence of Spanning k-Trees in Star-Free Graphs
Discussiones Mathematicae Graph Theory, 2022 For an integer k ≥ 2, a k-tree T is defined as a tree with maximum degree at most k. If a k-tree T spans a graph G, then T is called a spanning k-tree of G.
Furuya Michitaka +5 more
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On real or integral skew Laplacian spectrum of digraphs
, 2020 For a simple connected graph G with n vertices and m edges, let −→ G be a digraph obtained by giving an arbitrary direction to the edges of G . In this paper, we consider the skew Laplacian matrix of a digraph −→ G and we obtain the skew Laplacian ...
S. Pirzada +2 more
semanticscholar +1 more source
Special Matrices, 2017 We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue ...
Toyonaga Kenji, Johnson Charles R.
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Some improved bounds on two energy-like invariants of some derived graphs
Open Mathematics, 2019 Given a simple graph G, its Laplacian-energy-like invariant LEL(G) and incidence energy IE(G) are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. This paper obtains some improved bounds on LEL and
Cui Shu-Yu, Tian Gui-Xian
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Characteristic polynomials of some weighted graph bundles and its application to links
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 503-510, 1994., 1994 In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted ‐bundles over a weighted graph G? can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are G As an application, we compute the signature ...
Moo Young Sohn, Jaeun Lee
wiley +1 more source
Graphs Whose Aα -Spectral Radius Does Not Exceed 2
Discussiones Mathematicae Graph Theory, 2020 Let A(G) and D(G) be the adjacency matrix and the degree matrix of a graph G, respectively. For any real α ∈ [0, 1], we consider Aα (G) = αD(G) + (1 − α)A(G) as a graph matrix, whose largest eigenvalue is called the Aα -spectral radius of G.
Wang Jian Feng +3 more
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The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue
Special Matrices, 2023 Edges in the graph associated with a square matrix over a field may be classified as to how their removal affects the multiplicity of an identified eigenvalue.
Toyonaga Kenji
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Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Discussiones Mathematicae Graph Theory, 2020 A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths.
Liu Weijun +3 more
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Walks and eigenvalues of signed graphs
Special Matrices, 2023 In this article, we consider the relationships between walks in a signed graph G˙\dot{G} and its eigenvalues, with a particular focus on the largest absolute value of its eigenvalues ρ(G˙)\rho \left(\dot{G}), known as the spectral radius.
Stanić Zoran
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On the Skew Spectra of Cartesian Products of Graphs
Electronic Journal of Combinatorics, 2013 An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge of G a direction so that G becomes a directed graph.
Denglan Cui, Yaoping Hou
semanticscholar +1 more source