The average size of connected vertex subsets of a connected graph generalises a much‐
studied parameter for subtrees of trees. For trees, the possible values of this parameter are …

We make some fundamental observations and conjectures on the number of connected sets
$ N (G) $ in $ d $-regular graphs $ G $. We improve the best known lower bounds on the …

The topic is the average order of a connected induced subgraph of a graph. This
generalizes, to graphs in general, the average order of a subtree of a tree. In 1983, Jamison …

Although connectivity is a basic concept in graph theory, the enumeration of connected
subgraphs of a graph has only recently received attention. The topic of this paper is the …

We prove that among connected graphs of order n, the path uniquely minimises the average
order of its connected induced subgraphs. This confirms a conjecture of Kroeker, Mol and …

Because connectivity is such a basic concept in graph theory, extremal problems concerning
the average order of the connected induced subgraphs of a graph have been of notable …

In this paper we show that for a given $ k $-tree $ T $ with a $ k $-clique $ C $, the local
mean order of all sub-$ k $-trees of $ T $ containing $ C $ is not less than the global mean …

The topic is the average order A (G) of a connected induced subgraph of a graph G. This
generalizes, to graphs in general, the average order of a subtree of a tree. In 1983 Jamison …

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 …

In this paper we study the average order of dominating sets in a graph, avd (G) \,avd\,(G).
Like other average graph parameters, the extremal graphs are of interest. Beaton and Brown …