On regular graphs with a tree of diameter 3 as a star complement

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-03-17 DOI:10.1016/j.disc.2025.114488

Peter Rowlinson , Zoran Stanić

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引用次数: 0

Abstract

We investigate the regular graphs with a star complement H which is a tree of diameter 3. Thus H is a double star

D (m, n)

, i.e. a tree with two vertices of degree m and n greater than 1, and all other vertices of degree 1. We determine all the regular graphs G that arise when either (a)

μ \in {0, 1}

or (b)

m = n

and μ is an integer less than −1. It is also proved that for

m = n

and

μ \geq 2

, the degree of G must be n; moreover,

n \geq \frac{μ (μ (2 μ (μ + 1) - 3) + 3) - 1}{2 μ - 1},

when μ is an integer.

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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.