Energy of Some Extended Corona

For two graphs 𝐺_1 and 𝐺_2 with 𝑛 and 𝑚 vertices, the corona 𝐺_1 ∘ 𝐺_2 of 𝐺_1 and 𝐺_2 is defined as the graph obtained by taking one copy of 𝐺_1 and 𝑛 copies of 𝐺_2, and then joining the 𝑖 𝑡ℎ vertex of 𝐺_1 to every vertex in the 𝑖 𝑡ℎ copy of 𝐺_2. The neighborhood corona of 𝐺_1and 𝐺_2, denoted by 𝐺_1 ⋆ 𝐺_2 , is the graph obtained by taking one copy of 𝐺_1 and 𝑛 copies of 𝐺_2, and joining every neighbour of the 𝑖 𝑡ℎ vertex of 𝐺_1 to every vertex in the 𝑖 𝑡ℎ copy of 𝐺_2. In this paper we define extended corona, extended neighborhood corona, identity extended corona and identity extended neighbourhood corona of two graphs 𝐺_1 and 𝐺_2, (which are denoted by 𝐺_1 • 𝐺_2 , 𝐺_1 ∗ 𝐺_2 , 𝐼_{𝑒𝑥}(𝐺_1 ∘ 𝐺_2 (and 𝐼_{𝑒𝑥}(𝐺1 ⋆ 𝐺2 respectively. We compute an upper bound for their energy and the energy of the graph G is denoted by ε(G).