Infinite family of 3-connected cubic transmission irregular graphs

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Infinite family of 3-connected cubic transmission irregular graphs. / Dobrynin, Andrey A.

In: Discrete Applied Mathematics, Vol. 257, 31.03.2019, p. 151-157.

Research output: Contribution to journal › Article › peer-review

Harvard

Dobrynin, AA 2019, 'Infinite family of 3-connected cubic transmission irregular graphs', Discrete Applied Mathematics, vol. 257, pp. 151-157. https://doi.org/10.1016/j.dam.2018.10.036

APA

Dobrynin, A. A. (2019). Infinite family of 3-connected cubic transmission irregular graphs. Discrete Applied Mathematics, 257, 151-157. https://doi.org/10.1016/j.dam.2018.10.036

Vancouver

Dobrynin AA. Infinite family of 3-connected cubic transmission irregular graphs. Discrete Applied Mathematics. 2019 Mar 31;257:151-157. doi: 10.1016/j.dam.2018.10.036

Author

Dobrynin, Andrey A. / Infinite family of 3-connected cubic transmission irregular graphs. In: Discrete Applied Mathematics. 2019 ; Vol. 257. pp. 151-157.

BibTeX

@article{a75ddef57f174203b748b78079cf1256,

title = "Infinite family of 3-connected cubic transmission irregular graphs",

abstract = "Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees and 2-connected graphs were presented in Alizadeh and Klav{\v z}ar (2018) and Dobrynin (2019) [8, 9]. The following problem was posed in Alizadeh and Klav{\v z}ar (2018): do there exist infinite families of regular transmission irregular graphs? In this paper, an infinite family of 3-connected cubic transmission irregular graphs is constructed.",

keywords = "Graph invariant, Transmission irregular graph, Vertex transmission, Wiener complexity, TREES, WIENER INDEX, COMPLEXITY",

author = "Dobrynin, {Andrey A.}",

year = "2019",

month = mar,

day = "31",

doi = "10.1016/j.dam.2018.10.036",

language = "English",

volume = "257",

pages = "151--157",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Infinite family of 3-connected cubic transmission irregular graphs

AU - Dobrynin, Andrey A.

PY - 2019/3/31

Y1 - 2019/3/31

N2 - Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees and 2-connected graphs were presented in Alizadeh and Klavžar (2018) and Dobrynin (2019) [8, 9]. The following problem was posed in Alizadeh and Klavžar (2018): do there exist infinite families of regular transmission irregular graphs? In this paper, an infinite family of 3-connected cubic transmission irregular graphs is constructed.

AB - Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees and 2-connected graphs were presented in Alizadeh and Klavžar (2018) and Dobrynin (2019) [8, 9]. The following problem was posed in Alizadeh and Klavžar (2018): do there exist infinite families of regular transmission irregular graphs? In this paper, an infinite family of 3-connected cubic transmission irregular graphs is constructed.

KW - Graph invariant

KW - Transmission irregular graph

KW - Vertex transmission

KW - Wiener complexity

KW - TREES

KW - WIENER INDEX

KW - COMPLEXITY

UR - http://www.scopus.com/inward/record.url?scp=85057222947&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2018.10.036

DO - 10.1016/j.dam.2018.10.036

M3 - Article

AN - SCOPUS:85057222947

VL - 257

SP - 151

EP - 157

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -

ID: 17562952