Journals Information
Mathematics and Statistics Vol. 13(1), pp. 56 - 61
DOI: 10.13189/ms.2025.130107
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A Study on Laceability Partition Dimension of A Graph
Manjula M 1,*, Leena N Shenoy 2, Deepthy D 3
1 Research Scholar, Department of Mathematics, B.N.M.I.T., Bengaluru and Visvesvaraya Technological University, Belagavi, India
2 Research Supervisor, Department of Mathematics, B.N.M.I.T., Bengaluru and Visvesvaraya Technological University, Belagavi, India
3 Department of Mathematics, BGSCET, Bengaluru, Affiliated to Visvesvaraya Technological University, Belagavi, India
ABSTRACT
A Hamiltonian laceability is specifically studied for a bipartite graph. A bipartite graph is called Hamiltonian laceable if, for every pair of distinct vertices 
and 
, there is a Hamiltonian path between them. A graph 
with 
is Random Hamiltonian Laceable, if there exists a 
Hamiltonian path 
. In this paper, we present the concept of decomposing a graph into induced subgraphs such that each subgraph is random Hamiltonian laceable. This kind of partitioning can be obtained in many ways and the least number of partitions of vertex set such that the subgraph induced by each partition is random Hamiltonian laceable gives the Laceability Partition Dimension of a connected graph 
. Here, we examine the Laceability partition dimension for any simple, connected and non-bipartite graph G and it is denoted by 
. Obviously, each of these induced subgraphs ensures that there is always a path between any two vertices, which assists in routing and connectivity strategies in networking. It also reduces the redundant connections in networking. This technique in fact, gives a light to solving an NP-class problem of finding Hamiltonian cycle in a graph.
KEYWORDS
Hamiltonian Path, Random Hamiltonian Laceable, Laceability Partition Dimension, Friendship Graph, Fan Graph, Kite Graph, Butterfly Graph, Cube Connected Cycle Graph 
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Manjula M , Leena N Shenoy , Deepthy D , "A Study on Laceability Partition Dimension of A Graph," Mathematics and Statistics, Vol. 13, No. 1, pp. 56 - 61, 2025. DOI: 10.13189/ms.2025.130107.
(b). APA Format:
Manjula M , Leena N Shenoy , Deepthy D (2025). A Study on Laceability Partition Dimension of A Graph. Mathematics and Statistics, 13(1), 56 - 61. DOI: 10.13189/ms.2025.130107.