Abstract
Unicyclic graphs possessing Kekulé structures with minimal energy are considered. Let n and l be the numbers of vertices of graph and cycle C l contained in the graph, respectively; r and j positive integers. It is mathematically verified that for \(n \geqslant 6\) and l = 2r + 1 or \(l=4j+2, S_n^4\) has the minimal energy in the graphs exclusive of \(S_n^3\), where \(S_n^4\) is a graph obtained by attaching one pendant edge to each of any two adjacent vertices of C 4 and then by attaching n/2 − 3 paths of length 2 to one of the two vertices; \(S_n^3\) is a graph obtained by attaching one pendant edge and n/2 − 2 paths of length 2 to one vertex of C 3. In addition, we claim that for \(6 \leqslant n \leqslant 12, S_n^4\) has the minimal energy among all the graphs considered while for \(n\geqslant 14, S_n^3\) has the minimal energy.
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Wang, WH., Chang, A. & Lu, DQ. Unicyclic Graphs Possessing Kekulé Structures with Minimal Energy. J Math Chem 42, 311–320 (2007). https://doi.org/10.1007/s10910-006-9096-7
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DOI: https://doi.org/10.1007/s10910-006-9096-7