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131.
Ivan Gutman 《Monatshefte für Chemie / Chemical Monthly》2005,136(6):1055-1069
Summary. The fact that cyclic arrangements of double bonds have a dramatic effect on the behavior of conjugated organic molecules is known since the 19th century. The fact that in monocyclic conjugated systems the size of the cycle and the number of -electrons involved is decisive for their stability (aromaticity) or lack of stability (antiaromaticity) is known since the 1930s. In polycyclic -electron systems several cyclic effects are present simultaneously and their separation became possible only recently. A molecular orbital method has been elaborated, by means of which the energy effects of individual cycles in polycyclic -electron systems can be estimated. This method is briefly outlined and illustrated by pertinent examples. An exhaustive bibliography of the topic considered is given. 相似文献
132.
《Journal of Pure and Applied Algebra》2022,226(12):107134
The notion of a group action can be extended to the case of gyrogroups. In this article, we examine a digraph and graph associated with a gyrogroup action on a finite nonempty set, called a Schreier digraph and graph. We show that algebraic properties of gyrogroups and gyrogroup actions such as being gyrocommutative, being transitive, and being fixed-point-free are reflected in their Schreier digraphs and graphs. We also prove graph-theoretic versions of the three fundamental theorems involving actions: the Cauchy–Frobenius lemma (also known as the Burnside lemma), the orbit-stabilizer theorem, and the orbit decomposition theorem. Finally, we make a connection between gyrogroup actions and actions of symmetric groups by evaluation via Schreier digraphs and graphs. 相似文献
133.
《Discrete Mathematics》2022,345(3):112721
This paper studies thresholds in random generalized Johnson graphs for containing large cycles, i.e. cycles of variable length growing with the size of the graph. Thresholds are obtained for different growth rates. 相似文献
134.
《Discrete Mathematics》2022,345(5):112797
If the line graph of a graph G decomposes into Hamiltonian cycles, what is G? We answer this question for decomposition into two cycles. 相似文献
135.
《Discrete Mathematics》2022,345(5):112806
A sum graph is a finite simple graph whose vertex set is labeled with distinct positive integers such that two vertices are adjacent if and only if the sum of their labels is itself another label. The spum of a graph G is the minimum difference between the largest and smallest labels in a sum graph consisting of G and the minimum number of additional isolated vertices necessary so that a sum graph labeling exists. We investigate the spum of various families of graphs, namely cycles, paths, and matchings. We introduce the sum-diameter, a modification of the definition of spum that omits the requirement that the number of additional isolated vertices in the sum graph is minimal, which we believe is a more natural quantity to study. We then provide asymptotically tight general bounds on both sides for the sum-diameter, and study its behavior under numerous binary graph operations as well as vertex and edge operations. Finally, we generalize the sum-diameter to hypergraphs. 相似文献
136.
《Discrete Mathematics》2022,345(6):112832
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structures and techniques that generalize the circuit classification of the signed graphic frame matroid to any oriented hypergraphic incidence matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm is applied to oriented hypergraphs to provide a generalization of reorientation sets and frustration that is only well-defined on balanceable oriented hypergraphs. A simple partial characterization of unbalanceable circuits extends the applications to representable matroids demonstrating that the difference between the Fano and non-Fano matroids is one of balance. 相似文献
137.
《Discrete Mathematics》2022,345(9):112954
One of the remarkable contributions in the study of symmetric Cayley graphs on nonabelian simple groups is the complete classification of such graphs that are cubic and nonnormal. This naturally motivates the study of cubic (normal and nonnormal) symmetric bi-Cayley graphs on nonabelian simple groups. In this paper, the full automorphism groups of these graphs are determined, and necessary and sufficient conditions are given for a graph being a cubic normal symmetric Cayley or bi-Cayley graph on a nonabelian simple group (one may then find many examples). As an application, we also prove that cubic symmetric Cayley graphs on nonabelian simple groups are stable. 相似文献
138.
《Discrete Mathematics》2022,345(10):113028
We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs. 相似文献
139.
140.
设$ G $ 是一个$ n $ 阶$ k $ 圈图, $ k $ 圈图为边数等于顶点数加$ k-1 $ 的简单连通图。$ \mu_{1}(G) $ 、$ \mu_{2}(G) $ 分别记为图$ G $ 的Laplace矩阵的最大特征值和次大特征值, 图$ G $ 的Laplace分离度定义为$ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $ 。本文研究了给定阶数的$ k $ 圈图的最大Laplace分离度, 并刻画了相应的极图, 其结果推广了已有当$ k=1, 2, 3 $ 时的结论。 相似文献