Mathematics and Statistics Vol. 10(5), pp. 1127 - 1132
DOI: 10.13189/ms.2022.100524
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Characterization of a Class of Generalised Core-satellite Graphs Using Average Degree

Malathy V , Kalyani Desikan ^*
Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India

ABSTRACT

Network equilibrium models are significantly distinct in supply chain networks, traffic networks, and e-waste flow networks. The idea of network equilibrium is strongly perceived while determining the tuner sets of a graph (network). Tuner sets are subsets of vertices of the graph G whose degrees are lower than the average degree of G, d(G) that can compensate or balance the presence of vertices whose degrees are greater than d(G). Generalised core-satellite graph comprises copies of (the satellites) meeting in K_c (the core) and it belongs to the family of graphs of diameter two. It has a central core of vertices connected to a few satellites, where all satellite cliques need not be identical and can be of different sizes. Properties like hierarchical structure of large real-world networks, are competently modeled using core-satellite graphs [1, 2, 5]. This family of graphs exhibits the properties similar to scale-free network as they possess anomalous vertex connectivity, where a small fraction of vertices (the core) are densely connected. Since these graphs possess such a structural property, interesting results are obtained for these graphs when tuner sets are determined. In this paper, we have considered the graph , with p > q, a subclass of the generalized core-satellite graph which is a join of η copies of the clique K_q and γ copies of the clique K_p with the core K₁. We have obtained the tuner set for this subclass and established the relation between the Top T(G) and the cardinality of the tuner set through necessary and sufficient conditions. We analyze and characterize these graphs and obtain some interesting results while simultaneously examining the existence of tuner sets.

KEYWORDS
Network Equilibrium, Generalised Coresatellite Graphs, Graphs of Diameter Two, Average Degree, Tuner Set

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Malathy V , Kalyani Desikan , "Characterization of a Class of Generalised Core-satellite Graphs Using Average Degree," Mathematics and Statistics, Vol. 10, No. 5, pp. 1127 - 1132, 2022. DOI: 10.13189/ms.2022.100524.

(b). APA Format:
Malathy V , Kalyani Desikan (2022). Characterization of a Class of Generalised Core-satellite Graphs Using Average Degree. Mathematics and Statistics, 10(5), 1127 - 1132. DOI: 10.13189/ms.2022.100524.