Abstract
Graph invariants provide an amazing tool to analyze the abstract structures of networks. The interaction and interconnection between devices, sensors, and service providers have opened the door for an eruption of mobile over the web applications. Structure of web sites containing number of pages can be represented using graph, where web pages are considered to be the vertices, and an edge is a link between two pages. Figuring resolving partition of the graph is an intriguing inquest in graph theory as it has many applications such as sensor design, compound classification in chemistry, robotic navigation, and Internet network. The partition dimension is a graph parameter akin to the concept of metric dimension, and fault-tolerant partition dimension is an advancement in the line of research of partition dimension of the graph. In this paper, we compute fault-tolerant partition dimension of alternate triangular cycle, mirror graph, and tortoise graphs.
Highlights
Introduction and Basic TerminologiesGraph theory is an intense region of arithmetic that has capacious variety of implementations in numerous regions of science, such as chemistry, biology, software engineering, and electrical and hardware engineering
Authors conclude that pd(Ω) of alternate triangular cycle and tortoise graph for n ≥ 2 is 3
F(Ω) of alternate triangular cycle, mirror graph, and tortoise graph for n ≥ 2 is between 3 and 4. e obtained results led us to the conclusion that the discussed cyclic networks have constant partition and fault-tolerant partition dimension. pd(Ω) and F(Ω) of these graphs are independent of the number of vertices of the graph
Summary
Graph theory is an intense region of arithmetic that has capacious variety of implementations in numerous regions of science, such as chemistry, biology, software engineering, and electrical and hardware engineering. E metric dimension of Ω is defined as min|μ|: μ is resolving set of Ω and is denoted by β(Ω). E faulttolerant metric dimension of Ω is the minimum cardinality of fault-tolerant resolving set μ and is denoted by β′(Ω). Ahmad et al computed fault-tolerant metric dimension of P(n, 2) ⊙ K1 graph [3]. Ξp be a partition with p partition classes of vertex set of connected graph Ω. E concept of fault-tolerant partition dimension of the graph was initiated by Salman et al [22]. Ξp} be a partition with p partition classes of the vertex set of connected graph Ω. We extend this study by considering alternate triangular cycle, mirror graph, and tortoise graphs and show that they have constant fault-tolerant partition dimension.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
