Given a graph G=(V, E) G=(V,E) and a subset of its vertices V′⊆ VV^′⊆V, the subgraph
induced by V′ V^′ in G is that with vertex set V′ V^′ and edge set E′ E^′ formed by …

In this paper we prove several new lower bounds on the maximum number of leaves of a
spanning tree of a graph related to its order, independence number, local independence …

We discuss a new implementation of, and new experiments with, Fajtlowicz's Dalmatian
conjecture-making heuristic. Our program makes conjectures about relations of real number …

This paper introduces the\emph {Optimist}, an autonomous system developed to advance
automated conjecture generation in graph theory. Leveraging mixed-integer programming …

\emph {TxGraffiti} is a data-driven, heuristic-based computer program developed to
automate the process of generating conjectures across various mathematical domains …

We give a tight upper bound on the average distance of a connected graph of given order in
terms of its connected domination number. Our results are a strengthening of a result by …

This paper introduces the Optimist, an autonomous system developed to advanceautomated
conjecture generation in graph theory. Leveraging mixed-integer pro-gramming (MIP) and …

Recently, Kim and Shader analyzed the multiplicities of the eigenvalues of a Φ-binary tree.
We carry this discussion forward extending their results to a larger family of trees, namely …

We present Digenes, a new discovery system that aims to help researchers in graph theory.
While its main task is to find extremal graphs for a given (function of) invariants, it also …

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