The characteristic polynomial of a generalized join graph

Yu Chen and Haiyan Chen

Applied Mathematics and Computation, 2019, vol. 348, issue C, 456-464

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.

Keywords: The (generalized) characteristic polynomial; The generalized join graph; Cospectral (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318310543
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:456-464

DOI: 10.1016/j.amc.2018.12.013

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().