Enumerating simple paths from connected induced subgraphs

Abstract

We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets.

References in corpus (3)

• Algebraic combinatorics on trace monoids: extending number theory to walks on graphs
• Counting Paths and Packings in Halves
• The All-Paths and Cycles Graph Kernel

Cited by in corpus (1)

• Evaluating balance on social networks from their simple cycles