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

A Study on the Detour Self-Decomposition of Corona Product of Graphs | Chapter 11 | Mathematics and Computer Science: Contemporary Developments Vol. 10

A graph G is said to have a detour self-decomposition Π = (G₁,G₂,...,Gn) if every subgraph G_i,1 ≤ i ≤ n of G have the same detour number as the graph G. Detour self-decomposition number of a graph G as the maximum cardinality of the detour self-decomposition Π and is represented by the π_sdn(G). Detour self-decomposition on corona product of various graphs and the bounds of detour self-decomposition number are studied in this work.

 

Author (s) Details

 

Anlin Bena. E
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, Tamil Nadu-629 165, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamil Nadu-627012, India.

 

E. Ebin Raja Merly
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, Tamil Nadu-629 165, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v10/3266

Star-Rainbow Dynamic Coloring in Some Corona Product Graphs | Chapter 32 | Innovative Solutions: A Systematic Approach towards Sustainable Future

 Let G be a connected graph which is nontrivial, defined a coloring c: V(G)→ {1, 2,…., k}, k ∈N of the vertices of G. A rainbow dynamic coloring of a graph is adynamic coloring and minimum number of colors required, such that every pair ofvertices is connected by at least one path whose within vertices have different colors. Further, G is said to be star-rainbow dynamic colored if every path on four

vertices in it is rainbow dynamic colored. The minimum k for which there exist a k-vertex coloring called the star rainbow dynamic coloring of G, denoted by strrdyc(G). In this paper we determine some corona product graphs involving Petersen graph, path and complete graph, path and star graph and star and complete graph and find strrdyc(G) for such graphs.

Author (s) Details

Gayathri Annasagaram
Dayananfda Sagar Academy of Technology and Management, Bengaluru, Affiliated to Visvesvaraya Technological University Belagavi 590018, India.

R Murali
Dr. Ambedkar Institute of Technology, Bengaluru, Affiliated to Visvesvaraya Technological University Belagavi 590018, India.

Kulkarni Sunita Jagganathararao
Dr. Ambedkar Institute of Technology, Bengaluru, Affiliated to Visvesvaraya Technological University Belagavi 590018, India.

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-49238-47-3/CH32