On transmission-irregular graphs and long pendent paths

Ivan Damnjanović, Dragan Stevanović and Salem Al-Yakoob

Applied Mathematics and Computation, 2024, vol. 482, issue C

Abstract: The transmission of a vertex in a connected graph is the sum of distances from that vertex to all other vertices. A graph is transmission-irregular (TI) if no two of its vertices have the same transmission. Xu et al. (2023) [3] recently asked to establish methods for constructing new TI graphs from the existing ones and also about the existence of chemical TI graphs on every even order. We show that, under certain conditions, new TI graphs can be obtained from the existing TI graph G either by attaching pendent paths of equal length to every vertex of G or by attaching two pendent paths of consecutive lengths to one vertex of G. We also show the existence of chemical TI graphs for almost all even orders.

Keywords: Transmission-irregular graph; Pendent path; Vertex distances; Perfect squares; Chemical graph (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324003795
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:482:y:2024:i:c:s0096300324003795

DOI: 10.1016/j.amc.2024.128918

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().