On independent position sets in graphs





General position set, Independent set, Independent number, Independent position number


An independent set S of vertices in a graph G is an independent position set if no three vertices of S lie on a common geodesic. An independent position set of maximum size is an ip-set of G. The cardinality of an ip-set is the independent position number, denoted by ip(G). In this paper, we introduce and study the independent position number of a graph. Certain general properties of these concepts are discussed. Graphs of order n having the independent position number 1 or n − 1 are characterized. Bounds for the independent position number of Cartesian and Lexicographic product graphs are determined and the exact value for Corona product graphs are obtained. Finally, some realization results are proved to show that there is no general relationship between independent position sets and other related graph invariants

Author Biographies

Elias John Thomas, Mar Ivanios College

University of Kerala, Dept. of Mathematics.

Ullas Chandran S. V., Mahatma Gandhi College

University of Kerala, Dept. of Mathematics.


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How to Cite

E. J. Thomas and U. . Chandran S. V., “On independent position sets in graphs”, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 385-398, Mar. 2021.




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