TY - JOUR

T1 - Infinite family of 2-connected transmission irregular graphs

AU - Dobrynin, Andrey A.

N1 - Publisher Copyright: © 2018 Elsevier Inc.

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 -