Remoteness of graphs with given size and connectivity constraints

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-02-26 DOI:10.1016/j.disc.2025.114451

Peter Dankelmann , Sonwabile Mafunda , Sufiyan Mallu

引用次数: 0

Abstract

Let G be a finite, simple connected graph. The average distance of a vertex v of G is the arithmetic mean of the distances from v to all other vertices of G. The remoteness

ρ (G)

of G is the maximum of the average distances of the vertices of G.

In this paper, we give sharp upper bounds on the remoteness of a graph of given order, connectivity and size. We also obtain corresponding bound s for 2-edge-connected and 3-edge-connected graphs, and bounds in terms of order and size for triangle-free graphs.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.