Abstract
Let G=(V,E) be a connected graph. H denotes a family of pairwise disjoint graphs {Hv}v∈V. The Zykov sum of G and H, denoted by G[H], is the graph obtained from G by replacing every vertex v of G with graph Hv and all vertices of Hu,Hv are adjacent if uv∈E. In this paper, we first give a decomposition formula for the independence polynomial IG[H];x. Then, we derive a formula expressing the Fibonacci number of G[H] in terms of the independence polynomial of graph G and the Fibonacci number of Hv. Finally, as applications, we compute the independence polynomials and the Fibonacci numbers of several interesting graphs, such as the windmill graphs, the path network and the ring network.
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.
