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arXiv · 1811.05430

On the Mean Order of Connected Induced Subgraphs of Block Graphs

Kristaps J. Balodis·Matthew E. Kroeker·Lucas Mol·Ortrud R. Oellermann
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Abstract

The average order of the connected induced subgraphs of a graph $G$ is called the mean connected induced subgraph (CIS) order of $G$. This is an extension of the mean subtree order of a tree, first studied by Jamison. In this article, we demonstrate that among all connected block graphs of order $n$, the path $P_n$ has minimum mean CIS order. This extends a result of Jamison from trees to connected block graphs, and supports the conjecture of Kroeker, Mol, and Oellermann that $P_n$ has minimum mean CIS order among all connected graphs of order $n$.

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Kristaps J. Balodis, Matthew E. Kroeker, Lucas Mol, Ortrud R. Oellermann. 2018-11-13. On the Mean Order of Connected Induced Subgraphs of Block Graphs. https://arxiv.org/abs/1811.05430

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