DOI Link
https://doi.org/10.70013/3j5fkaao
Abstract
A graph H is said to be realizable by a graph G if for any vertex v in G, the induced subgraph of G on the neighborhood of v is isomorphic to H. In this paper, we show that a complete multipartite graph is realizable if and only if each of its parts has the same size; characterize the graphs by which a complete multipartite graph with each part having the same size is realizable; show that all cluster graphs are realizable; prove that a wheel is realizable if and only if it has four vertices; prove that a fan is realizable if and only if it has three vertices; and show that all friendship graphs are realizable. Also, we discuss the minimum number of vertices in G by which H is realizable.
Author ORCID Identifier
https://orcid.org/0009-0000-4485-8883
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Wang, Runze
(2025)
"On Realizability of Some Graphs,"
Communications on Number Theory and Combinatorial Theory: Vol. 6, Article 2.
DOI: 10.70013/3j5fkaao
Available at:
https://research.library.kutztown.edu/contact/vol6/iss1/2
