This paper explores the concept of range labeling applied to ladder graphs, which are a specific type of graph resembling a ladder structure. Range labeling is a method where labels, typically represented by integers, are assigned to the vertices of a graph such that certain conditions are satisfied. Specifically, the labels assigned to adjacent vertices must differ by at least a predetermined amount. Ladder graphs denoted as Ln where n represents the number of rungs, consist of two parallel paths with corresponding vertices connected by edges. The study systematically investigates the minimum and maximum range labeling requirements for ladder graphs, providing theoretical bounds and constructive algorithms. By examining the inherent properties of ladder graphs, such as their regularity and bipartite nature, we derive efficient labeling schemes. The findings contribute to a better understanding of range labeling in structured graphs and offer potential applications in areas such as network design, coding theory, and the scheduling of tasks.

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Range Labeling for Some Ladder Graphs

  • J. Senthamizh Selvan,
  • R. Jahir Hussain,
  • V. Mahalakshmi

摘要

This paper explores the concept of range labeling applied to ladder graphs, which are a specific type of graph resembling a ladder structure. Range labeling is a method where labels, typically represented by integers, are assigned to the vertices of a graph such that certain conditions are satisfied. Specifically, the labels assigned to adjacent vertices must differ by at least a predetermined amount. Ladder graphs denoted as Ln where n represents the number of rungs, consist of two parallel paths with corresponding vertices connected by edges. The study systematically investigates the minimum and maximum range labeling requirements for ladder graphs, providing theoretical bounds and constructive algorithms. By examining the inherent properties of ladder graphs, such as their regularity and bipartite nature, we derive efficient labeling schemes. The findings contribute to a better understanding of range labeling in structured graphs and offer potential applications in areas such as network design, coding theory, and the scheduling of tasks.