Characterizing Irregularity in Planar Graph Structures

Abdul Aleem Mughal; Raja Noshad Jamil; Abaid ur Rehman Virk

Author(s)

Abdul Aleem Mughal University of Management and Technology,Lahore,Pakistan

Raja Noshad Jamil University of Management and Technology,Lahore,Pakistan

Abaid ur Rehman Virk University of Management and Technology,Lahore,Pakistan

Abstract

Face irregularity strength under ? - labeling ? with class (a 1, ß 1, ? 1) of plane graphs is a labeling from the set of graph elements into the set of integers, that is, ? : {V ? E ? F } ? {1, 2, 3, .., ? }, such that the face weights are distinct at any stage in the graph labeling, that is, W? (a 1,ß 1,? 1)(f ) ?= W? (a 1,ß 1,? 1)(g), for any two faces f and g of the graph G. The face irregular strength of a plane graph G is the least possible integer ? such that G admits face irregular ? - labeling. In this research, authors have examined the exact tight lower bounds for the face irregular strength of generalized plane graphs under ? - labeling of class (a 1, ß 1, ? 1) for vertex (1, 0, 0), edge (0, 1, 0), face (0, 0, 1), vertex-face (1, 0, 1), edge-face (0, 1, 1) and entire (1, 1, 1). Results are veriefid by examples.

Publication Details

Page(s) 72-95

DOI DOI not available

Published Journal: Journal of Prime Research in Mathematics, Volume: 19, Issue: 2, Year: 2023

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Keywords

Cartesian product, Face weights, Face irregularity strength, Face labeling

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