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The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph G is called reciprocal if 1/≥ is an eigenvalue of G whenever λ is an eigenvalue of G. Further, if λ and 1 λ have the same multiplicities, for each eigenvalue λ, then it is called strong reciprocal. In (MATCH Commun. Math. Comput. Chem. 83 (2020) 631{633), it was conjectured that for every graph G with maximum degree Δ(G) and minimum degree ∞(G) whose adjacency matrix is non-singular, E(G) λ Δ(G) + ∞(G) and the equality holds if and only if G is a complete graph. Here, we prove the validity of this conjecture for some strong reciprocal graphs. Moreover, we show that if G is a strong reciprocal graph, then E(G) λ Δ(G) + ∞(G) - 1 2. Recently, it has been proved that if G is a reciprocal graph of order n and its spectral radius, ?, is at least 4λmin, where λmin is the smallest absolute value of eigenvalues of G, then E(G) λ n + 1 2. In this paper, we extend this result to almost all strong reciprocal graphs without the mentioned assumption. [ABSTRACT FROM AUTHOR]

The energy of a graph is the sum of the absolute values of the eigenvalues of a graph. Two graphs are said to be equienergetic if they have same energy. A graph is said to be complementary equienergetic if it is equienergetic with its complement. Recently several complementary equienergetic graphs have been identified. In this paper, we characterize the cycles, paths, complete bipartite regular graphs and iterated line graphs of regular graphs, which are complementary equienergetic. [ABSTRACT FROM AUTHOR]