2 research outputs found
Some results involving the -eigenvalues for graphs and line graphs
Let be a simple graph with adjacency matrix , signless Laplacian
matrix , degree diagonal matrix and let be the line graph
of . In 2017, Nikiforov defined the -matrix of , ,
as a linear convex combination of and , the following way,
where . In this
paper, we present some bounds for the eigenvalues of and for the
largest and smallest eigenvalues of . Extremal graphs attaining
some of these bounds are characterized.Comment: 18 pages, 5 figures, 3 table