Name
Abstract | ||
|---|---|---|
For a graph G with adjacency matrix A(G) and degree-diagonal matrix D(G), Cvetković et al introduced a bivariate polynomial ϕG(x,t)=det(xI−(A(G)−tD(G))), where I is the identity matrix. The polynomial ϕG(x, t) not only generalizes the characteristic polynomials of some well-known matrices related to G, such as the adjacency, the Laplacian matrices, but also has an elegant combinatorial interpretation as being equivalent to the Bartholdi zeta function. Let G=H[G1,G2,…,Gk] be the generalized join graph of G1,G2,…,Gk determined by graph H. In this paper, we first give a decomposition formula for ϕG(x, t). The decomposition formula provides us a new method to construct infinitely many pairs of non-regular ϕ-cospectral graphs. Then, as applications, explicit expressions for ϕG(x, t) of some special kinds of graphs are given. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.amc.2018.12.013 | Applied Mathematics and Computation |
Keywords | Field | DocType |
The (generalized) characteristic polynomial,The generalized join graph,Cospectral | Adjacency list,Adjacency matrix,Characteristic polynomial,Combinatorics,Riemann zeta function,Polynomial,Mathematical analysis,Matrix (mathematics),Identity matrix,Mathematics,Laplace operator | Journal |
Volume | ISSN | Citations |
348 | 0096-3003 | 0 |
PageRank | References | Authors |
0.34 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yu Chen | 1 | 3 | 1.40 |
| HaiYan Chen | 2 | 41 | 5.31 |