The determinant of a unicyclic graph’s neighborhood matrix
Copyright policy )The determinant of a unicyclic graph’s neighborhood matrix
Let \(G\) be a unicyclic graph with \(n\) vertices and a unique cycle, \(A(G)\) denotes the adjacency matrix of the graph \(G\). The algorithm for computing the determinant function of the matrix \(\alpha I_n+A(G)\) which uses \(O(n)\) arithmetic operations under some restrictions on the degrees of the vertices of the graph \(G\) is obtained. Among the corollaries from the above results the author points out the algorithms to compute the determinants of adjacency and neigborhood matrices and the characteristic polynomial for adjacency matrices.
- Hunan University of Science and Technology China (People's Republic of)
Numerical Analysis, algorithm, Algebra and Number Theory, adjacency matrix, Adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), Determinant, neighborhood matrix, Determinants, permanents, traces, other special matrix functions, Unicyclic graph, Neighborhood matrix, determinant, Numerical computation of determinants, Characteristic polynomial, Discrete Mathematics and Combinatorics, characteristic polynomial, Geometry and Topology, Paths and cycles, unicyclic graph
Numerical Analysis, algorithm, Algebra and Number Theory, adjacency matrix, Adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), Determinant, neighborhood matrix, Determinants, permanents, traces, other special matrix functions, Unicyclic graph, Neighborhood matrix, determinant, Numerical computation of determinants, Characteristic polynomial, Discrete Mathematics and Combinatorics, characteristic polynomial, Geometry and Topology, Paths and cycles, unicyclic graph
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!