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.

<abstract><p>Let $ A(G) and D(G) be the adjacency matrix degree diagonal of a graph G $, respectively. For any real number \alpha \in[0, 1] Nikiforov defined A_{\alpha} $-matrix as A_{\alpha}(G) = D(G)+(1-\alpha)A(G) $. Let S_k(A_{\alpha}(G)) sum k largest eigenvalues In this paper, some bounds on are obtained, which not only extends results signless Laplacian matrix, but it also gi...

Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with graph. In this paper, we show several NP-hard zero forcing numbers are not spectra types matrices particular, consider standard forcing, positive semidefinite and skew provide constructions infinite families pairs cospectral graphs, which different ...

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 ...

Let G be a simple graph with order n and size m. The quantity $$M_1(G)=\sum _{i=1}^{n}d^2_{v_i}$$ is called the first Zagreb index of G, where $$d_{v_i}$$ degree vertex $$v_i$$ , for all $$i=1,2,\dots ,n$$ . signless Laplacian matrix $$Q(G)=D(G)+A(G)$$ A(G) D(G) denote, respectively, adjacency diagonal degrees G. $$q_1\ge q_2\ge \dots \ge q_n\ge 0$$ eigenvalues largest eigenvalue $$q_1$$ spectr...

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

Let S(n, c) = K1∨(cK2∪(n−2c−1)K1), where n ≥ 2c+1 and c ≥ 0. In this paper, S(n, c) and its complement are shown to be determined by their Laplacian spectra, respectively. Moreover, we also prove that S(n, c) and its complement are determined by their signless Laplacian spectra, respectively.