TY: UNPB
T1 - The main vertices of a star set and related graph parameters
A1 - An?eli?, Milica
A1 - Cardoso, Domingos M.
A1 - Simi?, Slobodan K.
A1 - Stani?, Zoran
N2 - A vertex v ? V (G) is called ?-main if it belongs to a star set X ? V (G) of the
eigenvalue ? of a graph G and this eigenvalue is main for the graph obtained from
G by deleting all the vertices in X {v}; otherwise, v is ?-non-main. Some results
concerning main and non-main vertices of an eigenvalue are deduced. For a main
eigenvalue ? of a graph G, we introduce the minimum and maximum number of
?-main vertices in some ?-star set of G as new graph invariant parameters. The
determination of these parameters is formulated as a combinatorial optimization
problem based on a simplex-like approach. Using these and some related parameters
we develop new spectral tools that can be used in the research of the isomorphism
problem. Examples of graphs for which the maximum number of ?-main vertices
coincides with the cardinality of a ?-star set are provided.
UR - https://ria.ua.pt/handle/10773/30375
Y1 - 2020
PB - arXiv