Laceability Properties in Flower Snark Graphs

The metric dimension of a connected graph G is the smallest number of nodes (resolving set) required to identify all other nodes based on shortest path distances uniquely. The notion of resolving set is vital in robotic navigation and to create various plan of action for the mastermind game. If certain vertices of a set S ⊂ V(G) resolve each pair of nodes u and v of G, then that set is a resolving set. A metric basis represents the lowest number of nodes in the set S. In this study, we describe the distance matrix and metric dimension of sunflower graphs and flower snarks.

Section: Introductionmentioning

confidence: 99%

On metric dimensions of flower graphs

Girisha,

Rajendra,

Vijaya Chandra Kumar

et al. 2023

Hypo-edge-Hamiltonian laceability in Graphs

Neelannavar¹,

Girisha²

2020

Laceability on a class of line graph of cartesian product of graphs

Neelannavar¹,

Girisha

2021

Determining Hamiltonian path connectivity relationship among the nodes of the network increases its optimal connectivity. If a and b are nodes in a graph G so that d(a,b) = t and then P is a non-Hamilton path in G. G is referred to as K + r hypo -edge -Hamilton-t -laceable if P + re forms Hamilton path joining a and b, for each t for 1 ⩽ t ⩽ diamG. In this research article we investigate the hypo-edge-Hamilton laceability of line graph of Cartesian product of paths and cycles. Also we discuss the results on Cartesian product of path and wheel.