Year: 2026
Type: article
Abstract: In \(1973\), Harary and Palmer posed the problem of enumeration of labeled graphs on \(n \geq 1\) unisolated vertices and \(l \geq 0\) edges. In \(1997\), Bender et al. obtained a recurrence relation representing the sequence \(A054548\)(OEIS) of labeled graphs on \(n \geq 0\) unisolated vertices containing \(q \geq \frac{n}{2}\) edges. In \(2020\), Bhavale and Waphare obtained a recurrence relation representing the sequence of fundamental basic blocks on \(n \geq 0\) comparable reducible elements, having nullity \(l \geq \lfloor \frac{n+1}{2} \rfloor\). In this paper, we prove the equivalence of these two sequences. We also provide an edge labeling for a given vertex labeled finite simple graph.
Source: Congressus Numerantium
DOI: 10.61091/cn237-03
Author: A. N. Bhavale
Institution: Savitribai Phule Pune University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4406272858