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 ...

Suppose that the vertex set of a connected graph G is $$V(G)=\{v_1,\ldots ,v_n\}$$ . Then we denote by $$Tr_{G}(v_i)$$ sum distances between $$v_i$$ and all other vertices G. Let Tr(G) be $$n\times n$$ diagonal matrix with its (i, i)-entry equal to $$Tr_{G}(v_{i})$$ D(G) distance $$Q_{D}(G)=Tr(G)+D(G)$$ signless Laplacian The largest eigenvalues $$Q_D(G)$$ called spectral radius In this ...

Let f(D(i,j),di,dj) be a real function symmetric in i and j with the property that f(d,(1+o(1))np,(1+o(1))np)=(1+o(1))f(d,np,np) for d=1,2. G graph, di denote degree of vertex D(i,j) distance between vertices G. In this paper, we define f-weighted Laplacian matrix random graphs Erdös-Rényi graph model Gn,p, where p?(0,1) is fixed. Four weighted type energies: energy LEf(G), signless LEf+(G), in...