TY: UNPB
T1 - The H-join of arbitrary families of graphs
A1 - Cardoso, Domingos M.
A1 - Gomes, Helena
A1 - Pinheiro, Sofia J
N2 - 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.
UR - https://ria.ua.pt/handle/10773/30376
Y1 - 2021
PB - arXiv