Graphs, partitions and Fibonacci numbers

DOI10.1016/j.dam.2006.10.010zbMath1121.05031OpenAlexW2012356536MaRDI QIDQ2370416

Arnold Knopfmacher, Volker Ziegler, Stephan G. Wagner, Robert F. Tichy

Publication date: 26 June 2007

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2006.10.010

zbMATH Keywords

partitionindependent setFibonacci numberstar-like tree

Mathematics Subject Classification ID

Trees (05C05) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (18)

On Extremal Sombor Indices of Chemical Graphs, and Beyond ⋮ The Fibonacci numbers of certain subgraphs of circulant graphs ⋮ Maxima and minima of the Hosoya index and the Merrifield-Simmons index ⋮ Trees with given stability number and minimum number of stable sets ⋮ The second largest number of maximal independent sets in connected graphs with at most one cycle ⋮ Combinatorial Fiedler theory and graph partition ⋮ The cyclomatic number of a graph and its independence polynomial at \(- 1\) ⋮ On the connectivity properties and energy of Fibonomial graphs ⋮ Extremal problems for trees with given segment sequence ⋮ Independent vertex sets in the Zykov sum ⋮ A simple proof of an inequality connecting the alternating number of independent sets and the decycling number ⋮ A class of trees and its Wiener index ⋮ On the Fibonacci numbers of the composition of graphs ⋮ Trees with a given number of leaves and the maximal number of maximum independent sets ⋮ Perron values and classes of trees ⋮ Fibonacci index and stability number of graphs: a polyhedral study ⋮ Trees with the second largest number of maximal independent sets ⋮ Turán Graphs, Stability Number, and Fibonacci Index

Cites Work

• The number of maximal independent sets in a connected graph
• Independent sets in regular graphs and sum-free subsets of finite groups
• Bipartite graphs can have any number of independent sets
• The number of caterpillars
• The number of trees
• On the Number of Sum-Free Sets
• The Number of Maximal Independent Sets in a Tree
• A Note on Independent Sets in Trees
• The number of maximal independent sets in connected graphs
• Constraints on the number of maximal independent sets in graphs
• The Number of Independent Sets in a Grid Graph
• Independent Sets in Regular Hypergraphs and Multidimensional Runlength-Limited Constraints
• On cliques in graphs
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