Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

Version 1 : Received: 14 April 2021 / Approved: 15 April 2021 / Online: 15 April 2021 (12:31:09 CEST)
Version 2 : Received: 21 April 2021 / Approved: 21 April 2021 / Online: 21 April 2021 (12:46:29 CEST)

How to cite: Mughal, A.A.; Jamil, R.N. Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs. Preprints 2021, 2021040413 (doi: 10.20944/preprints202104.0413.v2). Mughal, A.A.; Jamil, R.N. Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs. Preprints 2021, 2021040413 (doi: 10.20944/preprints202104.0413.v2).

Abstract

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, fi nite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

Keywords

Total Face labeling of type (Alpha, Beta, Gamma); Total face irregularity strength; artesian product of path graphs; Graph Labeling; Graph theory

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (1)

Comment 1
Received: 21 April 2021
Commenter: Raja Noshad Jamil
Commenter's Conflict of Interests: Author
Comment: an eaxample added for explanation
theorm 2 upadeted

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