On The Center Sets and Center Numbers of Some Graph Classes
Ram Kumar. R, Kannan Balakrishnan, Manoj Changat, A.Sreekumar,, Prasanth G. Narasimha-Shenoi

TL;DR
This paper investigates the structure of center sets and introduces the concept of center number across various graph classes, providing enumeration and characterization results.
Contribution
It characterizes and enumerates center sets and center numbers for several graph classes, expanding understanding of graph center concepts.
Findings
Identified center sets for block graphs, complete bipartite graphs, wheel graphs, odd cycles, and symmetric even graphs.
Determined the center number for certain graph classes.
Provided enumeration methods for center sets in various graphs.
Abstract
For a set of vertices and the vertex in a connected graph , is called the -eccentricity of in . The set of vertices with minimum -eccentricity is called the -center of . Any set of vertices of such that is an -center for some set of vertices of is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, , , wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
