Geodesic
On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 127-140

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Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex in the i-th copy of H. The neighborhood corona G★H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. The edge corona G ◇ H is the graph obtained by taking one copy of G and |E(G)| copies of H and joining each terminal vertex of i-th edge of G to every vertex in the i-th copy of H. Let G1, G2, G3 and G4 be regular graphs with disjoint vertex sets. In this paper we compute the spectrum of (G1 ∨ G2) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ★ G4), (G1 ∨ G2) ∪ (G1 ○ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ○ G4), (G1 ∨ G2) ∪ (G1 ◇ G3), (G1 ∨ G2) ∪ (G2 ◇ G3) ∪ (G1 ◇ G4), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ◇ G4) and (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ◇ G4). As an application, we show that there exist some new pairs of equienergetic graphs on n vertices for all n ≥ 11.
Keywords: spectrum, corona, neighbourhood corona, edge corona, energy of a graph, equienergetic graphs 
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Adiga, Chandrashekar; Rakshith, B.R. On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 127-140. http://geodesic.mathdoc.fr/item/DMGT_2016_36_1_a9/