Infinite family of 2-connected transmission irregular graphs

Andrey A. Dobrynin

doi:10.1016/j.amc.2018.08.042

Infinite family of 2-connected transmission irregular graphs

Andrey A. Dobrynin

Лаборатория топологии и динамики ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

8 Цитирования (Scopus)

Аннотация

Distance between two vertices is the number of edges in the 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 were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

Язык оригинала	английский
Страницы (с-по)	1-4
Число страниц	4
Журнал	Applied Mathematics and Computation
Том	340
DOI	https://doi.org/10.1016/j.amc.2018.08.042
Состояние	Опубликовано - 1 янв 2019

Доступ к документу

10.1016/j.amc.2018.08.042

Link to publication in Scopus

Fingerprint Подробные сведения о темах исследования «Infinite family of 2-connected transmission irregular graphs». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать

@article{c4983f22181a409eb3b089e084e0d464,

title = "Infinite family of 2-connected transmission irregular graphs",

abstract = "Distance between two vertices is the number of edges in the 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 were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.",

keywords = "Transmission irregular graph, Vertex transmission, Wiener complexity, TREES, WIENER INDEX, COMPLEXITY, TOPOLOGICAL INDEXES",

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

year = "2019",

month = jan,

day = "1",

doi = "10.1016/j.amc.2018.08.042",

language = "English",

volume = "340",

pages = "1--4",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Science Inc.",

}

TY - JOUR

T1 - Infinite family of 2-connected transmission irregular graphs

AU - Dobrynin, Andrey A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Distance between two vertices is the number of edges in the 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 were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

AB - Distance between two vertices is the number of edges in the 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 were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

KW - Transmission irregular graph

KW - Vertex transmission

KW - Wiener complexity

KW - TREES

KW - WIENER INDEX

KW - COMPLEXITY

KW - TOPOLOGICAL INDEXES

UR - http://www.scopus.com/inward/record.url?scp=85052623394&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2018.08.042

DO - 10.1016/j.amc.2018.08.042

M3 - Article

AN - SCOPUS:85052623394

VL - 340

SP - 1

EP - 4

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -