The Determinant of the Adjacency Matrix of a Graph
From MaRDI portal
Publication:3850469
DOI10.1137/1004057zbMath0113.17406OpenAlexW1985911376WikidataQ56209825 ScholiaQ56209825MaRDI QIDQ3850469
Publication date: 1962
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/2e7333e33dcef8b4b3d18a94caaafd1e02a11244
Related Items
Inverses of non-bipartite unicyclic graphs with a unique perfect matching ⋮ Spectral moments of hypertrees and their applications ⋮ A graph-theoretic method for the basic reproduction number in continuous time epidemiological models ⋮ Unnamed Item ⋮ Applications of the Harary-Sachs theorem for hypergraphs ⋮ Relations between connected and self-avoiding hikes in labelled complete digraphs ⋮ Drum Shapes and Isospectral Graphs ⋮ Graph invertibility and median eigenvalues ⋮ On the adjacency matrix of a complex unit gain graph ⋮ Unnamed Item ⋮ On characteristic and permanent polynomials of a matrix ⋮ On the Characteristic Equations of the Characteristic Polynomial ⋮ Moore Graphs and Cycles Are Extremal Graphs for Convex Cycles ⋮ Automorphism groups of Cayley evolution algebras ⋮ Sensor fault detection and isolation via networked estimation: rank-deficient dynamical systems ⋮ The determinant of an antiadjacency matrix of a directed cycle graph with chords ⋮ A new expression for matching polynomials ⋮ Laplacian matching polynomial of graphs ⋮ Gröbner bases, symmetric matrices, and type C Kazhdan–Lusztig varieties ⋮ Parameterized complexity of determinant and permanent ⋮ On Randić energy ⋮ Permanental polynomials of graphs ⋮ Tree counting polynomials for labelled graphs. I: Properties ⋮ Odd 2-factored snarks ⋮ Hyperbolic surfaces with sublinearly many systoles that fill ⋮ Mathematical Aspects of Omega Polynomial ⋮ Unnamed Item ⋮ Input-Output Networks, Singularity Theory, and Homeostasis ⋮ On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree ⋮ Computation of maximum likelihood estimates in cyclic structural equation models ⋮ A reduction formula for the characteristic polynomial of hypergraph with pendant edges ⋮ A unified view on bipartite species-reaction graphs and their relation to interaction graphs and qualitative dynamics of chemical reaction networks ⋮ Balance in gain graphs - a spectral analysis ⋮ \(LDL^ T\) factorizations of adjacency matrices where \(D\) is block diagonal ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Rigid linkages and partial zero forcing ⋮ Spectrally arbitrary patterns over rings with unity ⋮ A formula for all minors of the adjacency matrix and an application ⋮ Isospectral polygons, planar graphs and heat content ⋮ Algorithms for finding directed graph isomorphisms by finite automata ⋮ Perfect graphs and complex surface singularities with perfect local fundamental group ⋮ Automorphism group and category of cospectral graphs ⋮ Two graphs with a common edge ⋮ A Harary-Sachs theorem for hypergraphs ⋮ On a conjecture about the μ-permanent ⋮ On the Number of Nonzeros Added when Gaussian Elimination is Performed on Sparse Random Matrices ⋮ SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM ⋮ Rectifying a misbelief: Frank Harary's role in the discovery of the coefficient-theorem in chemical graph theory ⋮ Integer LU-factorizations ⋮ Matrix measures for transitivity and balance* ⋮ The characteristic polynomial of a graph ⋮ A graph polynomial and its applications ⋮ Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics ⋮ On the multiple eigenvalue of Randić matrix of trees ⋮ Binomial incidence matrix of a semigraph ⋮ Some determinant expansions and the matrix-tree theorem ⋮ Characteristic power series of graph limits ⋮ On the spectral properties of Feigenbaum graphs