Minimum Independent Isolation Number of some Corona Product Graphs

Sambhu Charan Barman^1∗, Amita Samanta Adhya², Sukumar Mondal³, Mangal Pati⁴, Uma Shankar<sup>4

1</sup>Department of Mathematics, Shahid Matangini Hazra Government General Degree College for Women, Purba Medinipur – 721649, India.

²Department of BCA, Debra Thana Sahid Kshudiram Smriti Mahavidyalaya, Paschim Medinipur, India.

³Department of Mathematics, Raja N. L. Khan Women’s College (Autonomous), Midnapore – 721102, India.

⁴Department of Mathematics, Asian International University, Imphal West – 795113, India.

Abstract: The concept of isolation in graphs plays an important role in understanding the structural resilience and control mechanisms of networks. In this paper, we investigate the minimum independent isolation number of various corona product graphs such as P_n ⊙ P_m, P_n ⊙ C_m, K_n ⊙ K_m, P_n ⊙ K_m and P_n ⊙ S_m. An independent isolating set I of G is defined as a subset of the vertex set V of G in which no two vertices are adjacent and when removed I from the graph along with all their neighbors, only isolated vertices are left. An independent isolating set with smallest vertices is called a minimum independent isolating set. The independent isolation number of a graph G is the order of the minimum independent isolating set of G. We compute the minimum independent isolation number of P_n ⊙ P_m, P_n ⊙ C_m, K_n ⊙ K_m, P_n ⊙ K_m and P_n ⊙ S_m.

Key Words: article; template; simple