Results 21 to 30 of about 279 (161)
Enumeration of spanning trees in the sequence of Dürer graphs
Open Mathematics, 2017 In this paper, we calculate the number of spanning trees in the sequence of Dürer graphs with a special feature that it has two alternate states. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs ...
Li Shixing
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Rank relations between a {0, 1}-matrix and its complement
Open Mathematics, 2018 Let A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1.
Ma Chao, Zhong Jin
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Potential counter-examples to a conjecture on the column space of the adjacency matrix
Special MatricesAttempts to resolve the Akbari-Cameron-Khosrovshahi-conjecture have so far focused on the rank of a matrix. The conjecture claims that there exists a nonzero (0, 1)-vector in the row space of a (0, 1)-adjacency matrix A{\bf{A}} of a graph GG, that is not
Sciriha Irene +3 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.The polygonized graph Pn,k(G) is constructed from a simple connected graph G through a substitution process. During this process, each edge in G is replaced by one path of length 1 and k paths of length +1(n, k ≥ 1). Based on the properties of the determinants of tridiagonal matrices, we present a unified formula for computing the normalized Laplacian ...
Hao Li +3 more
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The minimum exponential atom-bond connectivity energy of trees
Special MatricesLet G=(V(G),E(G))G=\left(V\left(G),E\left(G)) be a graph of order nn. The exponential atom-bond connectivity matrix AeABC(G){A}_{{e}^{{\rm{ABC}}}}\left(G) of GG is an n×nn\times n matrix whose (i,j)\left(i,j)-entry is equal to ed(vi)+d(vj)−2d(vi)d(vj){e}^
Gao Wei
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Refined Lower Bounds for the Laplacian Estrada Index of Connected Graphs via the Two Largest Degrees
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let G be a graph with n vertices and Laplacian eigenvalues μ1, μ2, …, μn. The Laplacian Estrada index of G is defined as LEEG=eμ1+⋯+eμn. In this paper, using the Karush–Kuhn–Tucker optimization framework under inequality constraints, we establish new lower bounds for LEE(G) in terms of the two largest degrees of G.
Hamidreza Bamdad +3 more
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Degree‐Based Topological Indices of the Jacobson Graph of Zm×Zn×Zr
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let R be a commutative ring with unity. The Jacobson graph IR of R is an undirected simple graph whose vertex set is R\J(R), where J(R) is a Jacobson ideal of R, and for any distinct vertices x, y ∈ R\J(R) are adjacent if and only if 1 − xy is not a unit of R.
Ndago F. Omondi +2 more
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Cospectral Pairs of Regular Graphs with Different Connectivity
Discussiones Mathematicae Graph Theory, 2020 For vertex- and edge-connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
Haemers Willem H.
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Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations
Journal of Mathematics, Volume 2026, Issue 1, 2026.The energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix. This concept extends to various types of energies derived from different graph‐related matrices. This paper explores the spectral properties of Albertson energy and Albertson spectra.
Jane Shonon Cutinha +3 more
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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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