On complete multipartite orderenergetic graphs. (English) Zbl 1542.92226
Summary: S. Akbari et al. [MATCH Commun. Math. Comput. Chem. 84, No. 2, 325–334 (2020; Zbl 1473.92049)] defined orderenergetic graphs as those graphs whose energy is equal to their order. They observed that complete tripartite graphs \(K_{p, p, 6p}\) are orderenergetic for every \(p \geq 1\), and stated an expectation that these might be the only complete multipartite orderenergetic graphs with at least three parts. In this note we show the existence of infinitely many other families of such graphs with arbitrarily large number of parts, with \(K_{\underbrace{p, \dots, p}_{10\times}}\), \(40p\), being an example of such family with 11 parts.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C92 | Chemical graph theory |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
Citations:
Zbl 1473.92049Software:
Graph6JavaReferences:
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