Properties of Partial Complement Mycielskian Graph u (G)
Bhakti S. Bhadre, Jaishri B. Veeragoudar, Sunilkumar M. Hosamani · Annals of Pure and Applied Mathematics · 2023
For a graph ܩ with vertex set ܸሺܩሻ ൌ ሼݒ ଵ , ݒ ଶ , ݒ ଷ , … … ݒ ሽ the partial complement Mycielskian of graph ܩ is the graph ߤ | ሺܩሻ with vertex set ߤ | ൫ܸሺܩሻ൯ ൌ ܸ ∪ ܷ ∪ ሼݔሽ corresponding to each vertex ݒ in ܸሺܩሻ.Introduce a new vertex ݑ and let U =ݑ{ :1 ݅ ݊, ݒ ∈ ܸ and ݅ ൌ 1,2,3, … … ݊ሽ is a set disjoint from ܸ, take another vertex ݔ and add edges from ݔ to all vertices in U. ߤ൫ܧ | ሺܩሻ൯ ൌ ܧሺܩሻ ∪ ൛ݒ ݒ ݒ/ ݒ ∉ ܧሺܩሻൟ ∪ ݑ/ݑݔሼ ∈ ܷሽ.In this article, we explore the basic properties of the complement of the Mycielskian graph.