Results 21 to 30 of about 292 (163)

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
doaj   +1 more source

Potential counter-examples to a conjecture on the column space of the adjacency matrix

Special Matrices
Attempts 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, Kaur Bableen, Borg James L., Debono Mark   +3 more
doaj   +1 more source

On Generalized Harary Eigenvalues and Generalized Join of Graphs

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this work, we further study the generalized Harary matrix of a connected graph G, which we denote by RDα(G). This matrix is defined as the convex combination RDα(G) = αRT(G) + (1 − α)RD(G), where 0 ≤ α ≤ 1. In this formulation, RD(G) refers to the classical Harary matrix, and RT(G) represents a diagonal matrix of reciprocal transmission degrees of G.
Abdollah Alhevaz, Maryam Baghipur, Hilal A. Ganie, Yilun Shang, Xiaogang Liu   +4 more
wiley   +1 more source

The minimum exponential atom-bond connectivity energy of trees

Special Matrices
Let 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
doaj   +1 more source

Normalized Laplacian Spectrum and Graph Invariant Formulas of Polygonized Graphs Based on Tridiagonal Matrices

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, Xinyi Chen, Hao Liu, Pramita Mishra   +3 more
wiley   +1 more source

Spectral Characterization of the Eccentricity Matrix for Clean Graphs Over Rings of Specific Orders

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we study the eccentricity matrices of the clean graphs CLZp2 and CLZp⊕Zp. We begin by constructing these graphs and determining their eccentricity matrices. Then, we find the spectra of these matrices, that is, all eigenvalues together with their algebraic multiplicities.
Eman Rawshdeh, Heba Adel Abdelkarim, Edris Rawashdeh, A. Baniabedalruhman, Smritijit Sen   +4 more
wiley   +1 more source

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, Alireza Vahidi, Akram Mahmoodi, Smritijit Sen   +3 more
wiley   +1 more source

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
doaj   +1 more source

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.
doaj   +1 more source

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, Laithun Boro, Smritijit Sen   +2 more
wiley   +1 more source