In this paper we define extended corona and extended neighborhood corona of two graphs G 1 and G 2 , which are denoted by G 1 • G 2 and G 1 * G 2 respectively. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As applications, we give methods to construct infinite families of integral graphs, Laplacian integral graphs and expander graphs from known ones.
Abstract. In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary energy, maximum degree and minimum degree of a graph, and another bound in terms of forgotten index, inverse degree sum, order of a graph and minimum degree of a graph which improves an upper bound of Das et al. from [On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116-123]. We present a pair of extended equienergetic graphs on n vertices for n ≡ 0(mod 8) starting with a pair of extended equienergetic non regular graphs on 8 vertices and also we construct a pair of extended equienergetic graphs on n vertices for all n ≥ 9 starting with a pair of equienergetic regular graphs on 9 vertices.
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