On Transmission Irregular Cubic Graphs of an Arbitrary Order

On Transmission Irregular Cubic Graphs of an Arbitrary Order Full article

Journal

Mathematics
, E-ISSN: 2227-7390

Output data

Year: 2022, Volume: 10, Number: 15, Article number : 2741, Pages count : DOI: 10.3390/math10152741

Tags

cubic graph; graph invariant; transmission irregular graph; vertex transmission; Wiener complexity

Authors

Bezhaev A.Y. ¹ , Dobrynin A.A. ²

Affiliations

1	Institute of Computational Mathematics and Mathematical Geophysics, The Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
2	Sobolev Institute of Mathematics, The Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions. In 2018, Alizadeh and Klavžar posed the following question: do there exist infinite families of regular TI graphs? An infinite family of TI cubic graphs of order (Formula presented.), (Formula presented.), was constructed by Dobrynin in 2019. In this paper, we study the problem of finding TI cubic graphs for an arbitrary number of vertices. It is shown that there exists a TI cubic graph of an arbitrary even order (Formula presented.). Almost all constructed graphs are contained in twelve infinite families.

Bezhaev A.Y. , Dobrynin A.A.
On Transmission Irregular Cubic Graphs of an Arbitrary Order
Mathematics. 2022. V.10. N15. 2741 . DOI: 10.3390/math10152741 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 10, 2022
Accepted:	Jul 29, 2022
Published online:	Aug 3, 2022

Web of science:	WOS:000839739700001
Scopus:	2-s2.0-85136802491
Elibrary:	56130350
OpenAlex:	W4289731713

DB	Citing
Scopus	2
Web of science	2
OpenAlex	2