Extremal k‐uniform hypertrees on incidence energy

• Published in: International journal of quantum chemistry Vol. 121; no. 9
• Main Author: Zhu, Qiangyuan
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 05.05.2021; Wiley Subscription Services, Inc
• Subjects: Chemistry; Graph theory; incidence energy; k‐uniform hypergraph; Physical chemistry; Quantum physics; subdivision graph; Upper bounds
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.26592

For a k‐uniform hypergraph H = (V(H), E(H)), let B(H) be its incidence matrix, Q(H) = B(H)B(H)T be its signless Laplacian matrix. Let S(H) be the subdivision graph of H and AS be its adjacent matrix. For a matrix M, its energy E(M) is the sum of its singular values. The incidence energy BE(H) of H is the energy of B(H). In this article, we obtain some transformations on incidence energy, as their applications, the lower and upper bounds on BE(H) for hypertrees are obtained, at the same time, their corresponding extremal hypergraphs are characterized. As the generalization of graph, hypergraph has wider range of applications in real‐world. Naturally, the incidence energy of hypergraphs will have its own inherent advantages, that is to say, it is very meaningful to carry out research on it. Some new properties on incidence energy of hypergraphs given in this article will be useful in further studying on this topic.