The number of independent sets in unicyclic graphs
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TLDR
Upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order are determined and the extremal graphs are characterized.About:
This article is published in Discrete Applied Mathematics.The article was published on 2005-11-01 and is currently open access. It has received 81 citations till now. The article focuses on the topics: Independent set & Line graph.read more
Citations
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Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index
Stephan Wagner,Ivan Gutman +1 more
TL;DR: The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure as discussed by the authors.
A Unified Approach to the Extremal Zagreb Indices for Trees, Unicyclic Graphs and Bicyclic Graphs 1
TL;DR: In this article, a unified and simple approach to the largest and smallest Zagreb indices for trees, unicyclic graphs and bicyclic graphs was presented, and characterized for these graphs.
The extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index
Hanyuan Deng,Shubo Chen +1 more
TL;DR: The Hosoya index and the Merrifield-Simmons index of a graph are defined as the total number of its matchings and its independent sets, respectively.
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The Merrifield–Simmons Indices and Hosoya Indices of Trees with k Pendant Vertices
Aimei Yu,Xuezheng Lv +1 more
TL;DR: In this paper, the authors characterize the trees with maximal Merrifield-Simmons indices and minimal Hosoya indices, respectively, among trees with k pendant vertices.
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The Merrifield-Simmons index in (n, n + 1)-graphs
TL;DR: In this article, the upper bound for the Merrifield-Simmons index in (n, n + 1)−graphs in terms of the order n was determined.
References
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Journal ArticleDOI
On cliques in graphs
J. W. Moon,L. Moser +1 more
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Journal ArticleDOI
On the hardness of approximate reasoning
TL;DR: In this article, it was shown that the problem of estimating the number of satisfiability assignments is computationally intractable even if we settle for an approximation to the probability of a propositional expression being true.
Proceedings Article
On the hardness of approximate reasoning
TL;DR: It is proved that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited.
Book
Topological methods in chemistry
TL;DR: In this paper, the authors present a topological description of molecular structure bond topology graph topology duplex spaces topology of chemical reactions and a graph theory connectivity classification of topological spaces -separation axioms combinatorics functions and continuity.