Wheel graph

Wheel graph

Some New Graph Coloring Problems

Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020

A wheel graph, denoted by Wn, is a graph obtained by drawing edges between every vertex of a cycle Cn to an external vertex. That is, Wn = Cn + K1. Here Cn is called the rim of Wn. In view of Theorem 25.5, the rainbow neighbourhood number of Wn can be determined [12] as follows: For n ≥ 3, the rainbow neighbourhood number of a wheel graph Wn+1 = Cn + K1 is given by rχ(Wn+1)={4ifnisodd,n+1,ifniseven,Since the central vertex of the wheel graph is adjacent to all rim vertices, it will always be a rainbow neighbourhood vertex and hence the proof follows from the fact that rχ(Wn+1)=1+rχ(Cn).

Existence theorems for (Ψ,Φ)-orthogonal interpolative contractions and an application to fractional differential equations

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Journal Information

Published in Optimization, 2023

Muhammad Nazam, Hassen Aydi, Aftab Hussain

In graph theory, a wheel graph is a graph with n vertices for each , formed by connecting a single vertex to all vertices of an -cycle. Let be the set of all vertices of for each . Define if there is a connection from x to y. Then is an O-set.

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Some New Graph Coloring Problems

Existence theorems for (Ψ,Φ)-orthogonal interpolative contractions and an application to fractional differential equations