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Graphic and Cographic Г-Extensions of Binary Matroids
Discussiones Mathematicae Graph Theory, 2018 Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Г-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Г-extension operation the properties like
Borse Y.M., Mundhe Ganesh
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Graphs With All But Two Eigenvalues In [−2, 0]
Discussiones Mathematicae Graph Theory, 2020 The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0.
Abreu Nair +4 more
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Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph
Discussiones Mathematicae Graph Theory, 2022 Given a signed graph Ġ, let AĠ and DG˙±D_{\dot G}^ \pm denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of Ġ is defined to be NG˙=DG˙±-AG˙{N_{\dot G}} = D_{\dot G}^ \pm - {A_{\dot
Stanić Zoran
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Degree Subtraction Adjacency Eigenvalues and Energy of Graphs Obtained From Regular Graphs
Open Journal of Discrete Applied Mathematics, 2018 Let V (G) = {v1, v2, . . . , vn} be the vertex set of G and let dG(vi) be the degree of a vertex vi in G. The degree subtraction adjacency matrix of G is a square matrix DSA(G) = [dij ], in which dij = dG(vi) − dG(vj), if vi is adjacent to vj and dij = 0,
H. Ramane, Hemaraddi N. Maraddi
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On the Eccentric Spectra of the Line Graph of Starlike Trees
Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.A tree is called starlike if it has exactly one vertex with a degree greater than two. In this paper, we determine the eccentricity spectrum of the line graphs of starlike trees and compute their eccentric energy. Furthermore, we establish that the eccentricity matrix of the line graph of any starlike tree is irreducible.
S. Balamoorthy +4 more
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Graphs whose Laplacian eigenvalues are almost all 1 or 2
Special MatricesWe explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
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Turán’s Theorem Implies Stanley’s Bound
Discussiones Mathematicae Graph Theory, 2020 Let G be a graph with m edges and let ρ be the largest eigenvalue of its adjacency matrix.
Nikiforov V.
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Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi +3 more
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Open problems on graph eigenvalues studied with AutoGraphiX
EURO Journal on Computational Optimization, 2013 Since the late forties of the last century, methods of operations research have been extensively used to solve problems in graph theory, and graph theory has been extensively used to model operations research problems and to solve optimization problems ...
Mustapha Aouchiche +2 more
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On Singular Signed Graphs with Nullspace Spanned by a Full Vector: Signed Nut Graphs
Discussiones Mathematicae Graph Theory, 2022 A signed graph has edge weights drawn from the set {+1, −1}, and is sign-balanced if it is equivalent to an unsigned graph under the operation of sign switching; otherwise it is sign-unbalanced.
Bašić Nino +3 more
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