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《Discrete Mathematics》2023,346(6):113349
The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations. 相似文献
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Ronald L. Persky 《International Journal of Mathematical Education in Science & Technology》2013,44(6):927-928
In 1968, Leon Gerber compared (1 + x) a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented. 相似文献
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Abstract The novel Cluj property indices are used for modeling the biological properties of dipeptides: the ACE inhibition activity of a set of 58 dipeptides and the bitter tasting activity of a set of 48 dipeptides, taken from the literature. The results are compared to those reported in some previous works. 相似文献
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In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(9):3313-3322
This paper addresses the bipartite flock control problem where a multi-agent system splits into two clusters upon internal or external excitations. Using structurally balanced signed graph theory, LaSalle’s invariance principle and Barbalat’s Lemma, we prove that the proposed algorithm guarantees a bipartite flocking behavior. In each of the two disjoint clusters, all individuals move with the same direction. Meanwhile, every pair of agents in different clusters moves with opposite directions. Moreover, all agents in the two separated clusters approach a common velocity magnitude, and collision avoidance among all agents is ensured as well. Finally, the proposed bipartite flock control method is examined by numerical simulations. The bipartite flocking motion addressed by this paper has its references in both natural collective motions and human group behaviors such as predator–prey and panic escaping scenarios. 相似文献
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Let G be a 2k-edge-connected graph with and let for every . A spanning subgraph F of G is called an L-factor, if for every . In this article, we show that if for every , then G has a k-edge-connected L-factor. We also show that if and for every , then G has a k-edge-connected L-factor. 相似文献