Maximum energy bicyclic graphs containing two odd cycles with one common vertex

The energy of a graph is the sum of the absolute values of all eigenvalues of its adjacency matrix. Let P-n(6,6) be the graph obtained from two copies of C-6 joined by a path Pn-10. In 2001, Gutman and Vidovi & cacute; (2001) conjectured that the bicyclic graph with the maximal energy is P-n(6,6). This conjecture is true for bipartite bicyclic graphs. For non-bipartite bicyclic graphs, Ji and Li (2012) proved the conjecture for bicyclic graphs which have exactly two edge-disjoint cycles such that one of them is even and the other is odd. This paper is to prove the conjecture for bicyclic graphs containing two odd cycles with one common vertex. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining ,AI training, and similar technologies.