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...

In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined by taking corona product of the basic ...

Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian properties of graphs. 2010Mathematics Subject Classification : 05C50, 05C45