Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 3, pp. 41 – 56
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0093
Chromatically unique \(6\)-bridge graph \(\theta (r,r,s,s,t,u)\)
Syed Ahtsham Ul Haq Bokhary\(^{1,*}\), Shehr Bano
\(^{1}\)Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Copyright © 2023 Syed Ahtsham Ul Haq Bokhary and Shehr Bano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: July 18, 2023 – Accepted: December 25, 2023 – Published: December 27, 2023
Abstract
Let \(A\) and \(B\) be two graph and \(P(A,z)\) and \(P(B,z)\) are their chromatic polynomial, respectively. The two graphs \(A\) and \(B\) are said to be chromatic equivalent denoted by \( A \sim B \) if \(P(A,z)=P(B,z)\). A graph \(A\) is said to be chromatically unique(or simply \(\chi\)- unique) if for any graph \(B\) such that \(A\sim B \), we have \(A\cong B\), that is \(A\) is isomorphic to \(B\). In this paper, the chromatic uniqueness of a new family of \(6\)-bridge graph \(\theta(r,r,s,s,t,u)\) where \(2\leq r\leq s \leq t\leq u\) is investigated.
Keywords:
Chromatic polynomial; Chromatically unique; multi-bridge
graph.
graph.