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http://hdl.handle.net/10773/30376
Title: | The H-join of arbitrary families of graphs |
Author: | Cardoso, Domingos M. Gomes, Helena Pinheiro, Sofia J |
Keywords: | H-join Lexicographic product Graph spectra |
Issue Date: | 21-Jan-2021 |
Publisher: | arXiv |
Abstract: | The H-join of a family of graphs G = {G1, . . . , Gp}, also called the generalized composition, H[G1, . . . , Gp], where all graphs are undirected, simple and finite, is the graph obtained from the graph H replacing each vertex i of H by Gi and adding to the edges of all graphs in G the edges of the join Gi ∨ Gj , for every edge ij of H. Some well known graph operations are particular cases of the H-join of a family of graphs G as it is the case of the lexicographic product (also called composition) of two graphs H and G, H[G], which coincides with the H-join of family of graphs G where all the graphs in G are isomorphic to a fixed graph G. So far, the known expressions for the determination of the entire spectrum of the H-join in terms of the spectra of its components and an associated matrix are limited to families of regular graphs. In this paper, we extend such a determination to families of arbitrary graphs. |
Peer review: | no |
URI: | http://hdl.handle.net/10773/30376 |
Publisher Version: | https://arxiv.org/abs/2101.08383 |
Appears in Collections: | CIDMA - Artigos DMat - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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arXiv2101.08383.pdf | 190.95 kB | Adobe PDF | View/Open |
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