On the Steiner Radial Number of Graphs

Kathiresan, K.; Arockiaraj, S.; Gurusamy, R.; Amutha, K.

doi:10.1007/978-3-642-35926-2_7

Cited by 3 publications

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…KM. Kathiresan et al [10] initiated the concept of Steiner radial number of a graph G. The idea of antipodal graph was introduced by Singleton [13] and was further developed by R. Aravamudhan and B. Rajendran [1,2] and E. Prisner [12].…”

Section: Introductionmentioning

confidence: 99%

On the Steiner antipodal number of graphs

Arockiaraja¹,

Gurusamy²,

Kathiresan³

2019

ejgta

Self Cite

View full text Add to dashboard Cite

The Steiner n-antipodal graph of a graph G on p vertices, denoted by SA n (G), has the same vertex set as G and any n(2  n  p) vertices are mutually adjacent in SA n (G) if and only if they are n-antipodal in G. When G is disconnected, any n vertices are mutually adjacent in SA n (G) if not all of them are in the same component. SA n (G) coincides with the antipodal graph A(G) when n = 2. The least positive integer n such that SA n (G) ⇠ = H, for a pair of graphs G and H on p vertices, is called the Steiner A-completion number of G over H. When H = K p , the Steiner A-completion number of G over H is called the Steiner antipodal number of G. In this article, we obtain the Steiner antipodal number of some families of graphs and for any tree. For every positive integer k, there exists a tree having Steiner antipodal number k and there exists a unicyclic graph having Steiner antipodal number k. Also we show that the notion of the Steiner antipodal number of graphs is independent of the Steiner radial number, the domination number and the chromatic number of graphs.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Steiner antipodal number of graphs

Arockiaraja¹,

Gurusamy²,

Kathiresan³

2019

ejgta

Self Cite

View full text Add to dashboard Cite

show abstract

The total Steiner number of a graph

John¹

2020

Discrete Math. Algorithm. Appl.

View full text Add to dashboard Cite

A total Steiner set of [Formula: see text] is a Steiner set [Formula: see text] such that the subgraph [Formula: see text] induced by [Formula: see text] has no isolated vertex. The minimum cardinality of a total Steiner set of [Formula: see text] is the total Steiner number of [Formula: see text] and is denoted by [Formula: see text]. Some general properties satisfied by this concept are studied. Connected graphs of order [Formula: see text] with total Steiner number 2 or 3 are characterized. We partially characterized classes of graphs of order [Formula: see text] with total Steiner number equal to [Formula: see text] or [Formula: see text] or [Formula: see text]. It is shown that [Formula: see text]. It is shown that for every pair k, p of integers with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text]. Also, it is shown that for every positive integer [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text], there exists a connected graph [Formula: see text] of order [Formula: see text] such that [Formula: see text] and [Formula: see text].

show abstract

The total edge Steiner number of a graph

John¹

2021

AUCMCS

View full text Add to dashboard Cite

A total edge Steiner set of G is an edge Steiner set W such that the subgraph <W> induced by has no isolated vertex. The minimum cardinality of a total edge Steiner set of G is the total edge Steiner number of G and is denoted by ste(G). Some general properties satisfied by this concept are studied. The total edge Steiner numbers of certain classes of graphs is studied. Connected graphs of order p with total edge Steiner number 2 or 3 are characterized. Necessary conditions for total edge Steiner number to be p or p − 1 is given. It is shown that for every pair a and b of integers with 2 ≤ a < b and b > a+ 1, there exists a connected graph G such that se(G) = a and ste(G) = b. Also it shown that for every pair a and b of integers with 4 ≤ a < b and b > a + 1, there exists a connected graph G such that st(G) = a and ste(G) = b.

show abstract

On the Steiner Radial Number of Graphs

Cited by 3 publications

References 2 publications

On the Steiner antipodal number of graphs

On the Steiner antipodal number of graphs

The total Steiner number of a graph

The total edge Steiner number of a graph

Contact Info

Product

Resources

About