Carla Silva Oliveira

Bounds on the index of the signless Laplacian of a graph

A shock absorber apparatus connected in series relationship respective to the polished rod and bridle of a pumpjack unit. The shock absorber includes a housing within which there is supported a plurality of resilient packer members stacked in sandwiched relationship. The packer members have an axial passageway formed therethrough, with the passageway of each packer member being aligned with one another, so that the polished rod is telescopingly received therethrough. The bottom of the housing is supported by the bridle, while the polished rod is supported by a plate member which bears against the uppermost packer member. This places all of the resilient packer members in compression, with the force of the compression being proportional to the weight of the sucker rod.

The characteristic polynomial of the Laplacian of graphs in (a,b)-linear classes

In this work we deal with the characteristic polynomial of the Laplacian of a graph. We present some general results about the coefficients of this polynomial. We present families of graphs, for which the number of edges m is given by a linear function of the number of vertices n. In some of these graphs we can find certain coefficients of the above-named polynomial as functions just of n.

Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity

The algebraic connectivity a(G) of a graph G = (V, E) is the second smallest eigenvalue of its Laplacian matrix. Using the AutoGraphiX (AGX) system, extremal graphs for algebraic connectivity of G in function of its order n = |V| and size m = |E| are studied. Several conjectures on the structure of those graphs, and implied bounds on the algebraic connectivity, are obtained. Some of them are proved, e.g., if G ≠ K n

Parameters of connectivity in (a,b)-linear graphs

a\left( G \right) \leqslant \left\lfloor { - 1 + \sqrt {1 + 2m} } \right\rfloor

The non-bipartite graphs with all but two eigenvalues in [–1, 1]

which is sharp for all m ≥ 2.

Measures of irregularity of graphs

Let G be a simple graph on

A lower bound for the sum of the two largest signless Laplacian eigenvalues

n

The smallest eigenvalue of the signless Laplacian

vertices and