A lower bound on the average size of a connected vertex set of a graph

DOI10.1016/j.jctb.2021.09.008zbMath1478.05085arXiv2103.15174OpenAlexW3206911711MaRDI QIDQ2664553

Andrew Vince

Publication date: 17 November 2021

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.15174

zbMATH Keywords

average ordergraph connectedness

Mathematics Subject Classification ID

Trees (05C05) Connectivity (05C40) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (4)

The number and average size of connected sets in graphs with degree constraints ⋮ On the local and global mean orders of sub-\(k\)-trees of \(k\)-trees ⋮ The average size of a connected vertex set of a \(k\)-connected graph ⋮ The path minimises the average size of a connected induced subgraph

Cites Work

• Extremal results on average subtree density of series-reduced trees
• Monotonicity of the mean order of subtrees
• Enumeration of subtrees of trees
• The average order of a subtree of a tree
• Graphs of maximum diameter
• On the average number of nodes in a subtree of a tree
• On the Local and Global Means of Subtree Orders
• The mean order of sub‐k‐trees of k‐trees
• On the Mean Connected Induced Subgraph Order of Cographs
• On the Mean Order of Connected Induced Subgraphs of Block Graphs
• Maximizing the mean subtree order
• The average size of a connected vertex set of a graph—Explicit formulas and open problems
• The number and average size of connected sets in graphs with degree constraints

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