Extremal results on stepwise transmission irregular graphs-Reference-Cited by-同舟云学术

Extremal results on stepwise transmission irregular graphs

Published:2023 Issue:4 Volume:37 Page:1271-1276
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Alizadeh Yaser¹,Klavzar Sandi²

Affiliation:

1. Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran

2. Faculty of Mathematics and Physics, University of Ljubljana, Slovenia + Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia + Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

Abstract

The transmission TrG(v) of a vertex v of a connected graph G is the sum of distances between v and all other vertices in G. G is a stepwise transmission irregular (STI) graph if |TrG(u) ? TrG(v)| = 1 holds for each edge uv ? E(G). In this paper, extremal results on STI graphs with respect to the size and different metric properties are proved. Two extremal families appear in all the cases, balanced complete bipartite graphs of odd order and the so called odd hatted cycles.

Publisher

National Library of Serbia

Subject

General Mathematics

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