Laceability Partition Dimension of Some Special Graphs

Objectives: Laceability partition dimension of a connected graph is the minimum number of partitions of vertex set such that the subgraph induced by each partition is laceable in the case of a bipartite graph and random Hamiltonian laceable in case of non-bipartite graph . Methods: Mathematical Induction method and tracing Hamiltonian path. Findings: This study presents the laceability partition dimension (lpd) of some special graphs namely the Crown graph, Windmill graph, Dutch windmill graph, Cocktail party graph, shadow graph, and image graph. Novelty: This study discusses the laceability partition dimension of the graphs through which we discover a Hamiltonian path within a smaller structure whenever Hamiltonian laceability doesn't exist in large networks which has significance in communication networking that strives for optimal message routing efficiency. Keywords: Hamiltonian path, Bipartite graph, Laceability, Perfect matching, Shadow distance graph