An Improved Upper Bound for Steiner Decomposition Number | Chapter 4 | Mathematics and Computer Science: Contemporary Developments Vol. 8

For a connected graph G with Steiner number s(G), a decomposition π= {G₁, G₂, …,G_n} is said to be a Steiner decomposition if s(G_i )=s(G) for 1 ≤I ≤ n. The maximum cardinality obtained for π is called the Steiner decomposition number and it is denoted as π_st (G) [1]. In this paper, a new parameter for connected graph G denoted by q(G') is introduced. The parameter q(G') denotes the number of edges of G' which is the connected subgraph of G of minimum size having Steiner number same as G. This parameter provides an improved upper bound for the Steiner decomposition number. Here, some properties of graphs based on q(G') and the value of this parameter for the corona product of graphs are presented.

 

Author (s) Details

 

Ebin Raja Merly E
Department of Mathematics, Nesamony Memorial Christian College, Marthandam-629165, Tamil Nadu, India.

 

Mahiba M
Department of Mathematics, St. Alphonsa College of Arts and Science, Karinkal-629157, Tamil Nadu, India and Manonmanium Sundaranar University, Tirunelveli-627012, Tamil Nadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v8/2940