Let D be a digraph with n vertices and arcs. The Laplacian the signless matrices of are, respectively, defined as L(D)=Deg+(D)−A(D) Q(D)=Deg+(D)+A(D), where A(D) represents adjacency matrix Deg+(D) diagonal whose elements are out-degrees in D. We derive combinatorial representation regarding first few coefficients (signless) characteristic polynomial provide concrete directed motifs to highligh...

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are ...

The aim is to predict the labeling of the vertices of a graph. The graph is given. A trial sequence of (vertex,label) pairs is then incrementally revealed to the learner. On each trial a vertex is given and the learner predicts a label and then the true label is returned. The learner’s goal is to minimize mistaken predictions. We propose to solve the problem by the method of best approximation....

a concept related to the spectrum of a graph is that of energy. the energy e(g) of a graph g is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of g . the laplacian energy of a graph g is equal to the sum of distances of the laplacian eigenvalues of g and the average degree d(g) of g. in this paper we introduce the concept of laplacian energy of fuzzy graphs. ...