Yaser Alizadeh, Nino Bašić, Ivan Damnjanović, Tomislav Došlić, Tomaž Pisanski, Dragan Stevanović, Kexiang Xu
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引用次数: 0
摘要
如果存在一个图 G，使得 \(I(G) = p\) ，那么一个非负整数 p 就可以通过图论不变式 I 来实现。在本文中，我们考虑并解决了莫斯塔尔指数的逆问题。莫斯塔尔指数是最近引入的图论不变式，近年来在数学界和化学界引起了广泛关注。我们证明，当且仅当莫斯塔尔指数不等于 1 时，一个非负整数是可以通过莫斯塔尔指数实现的。除了提出问题的完整解决方案，我们还提出了一些经验观察，并概述了几个未决问题和可能的进一步研究方向。
A nonnegative integer p is realizable by a graph-theoretical invariant I if there exists a graph G such that \(I(G) = p\). The inverse problem for I consists of finding all nonnegative integers p realizable by I. In this paper, we consider and solve the inverse problem for the Mostar index, a recently introduced graph-theoretical invariant which attracted a lot of attention in recent years in both the mathematical and the chemical community. We show that a nonnegative integer is realizable by the Mostar index if and only if it is not equal to one. Besides presenting the complete solution to the problem, we also present some empirical observations and outline several open problems and possible directions for further research.
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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