Abstract
It is well known that many topological indices have widespread use in lots of fields about scientific research, and the Kirchhoff index plays a major role in many different sectors over the years. Recently, Li et al. (Appl. Math. Comput. 382 (2020) 125335) proposed the problem of determining the Kirchhoff index and multiplicative degree‐Kirchhoff index of graphs derived from Sn × K2, the Cartesian product of the star Sn, and the complete graph K2. In the present study, we completely solve this problem, that is, the explicit closed‐form formulae of the Kirchhoff index, multiplicative degree‐Kirchhoff index, and number of spanning trees are obtained for some graphs derived from Sn × K2.
Highlights
For two vertices vi and vj, the distance between them written as dij is the length of the shortest path linking them
Explicit expressions of the above index have been derived for linear polyomino chain [19], linear crossed polyomino chain [20], linear pentagonal chain
Li et al [38] determined the expressions of Kf(Sr), Kf∗(Sr), and τ(Sr), where Sr is a graph derived from Sn ⊗ K2 by randomly removing r vertical edges, and τ(G) denotes the number of spanning trees of a connected graph G. They proposed the problem of determining these three invariants for graphs derived from Sn × K2
Summary
For two vertices vi and vj, the distance between them written as dij is the length of the shortest path linking them. We suppose that G (V, E) is a nontrivial simple and connected graph, where V v1, v2, . One of the most famous results is the Kirchhoff index, which is used to characterize the structure of a compound. E Kirchhoff index of G is written as Kf(G) i
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
