TY - JOUR

T1 - A new generalization of edge-irregular evaluations

AU - Bača, Martin

AU - Imran, Muhammad

AU - Kimáková, Zuzana

AU - Semaničová-Feňovčíková, Andrea

N1 - Publisher Copyright:
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0).

PY - 2023

Y1 - 2023

N2 - Consider a simple graph G = (V, E) of size m with the vertex set V and the edge set E. A modular edge-irregular total k-labeling of a graph G is a labeling scheme for the vertices and edges with the labels 1, 2, …, k that allows the modular weights of any two different edges to be distinct, where the modular weight of an edge is the remainder of the division of the weight (i.e., the sum of the label of the edge itself and the labels of its two end vertices) by m. The maximal integer k, minimized over all modular edge-irregular total k-labelings of the graph G is called the modular total edge-irregularity strength. In the paper, we generalize the approach to edge-irregular evaluations, introduce the notion of the modular total edge-irregularity strength and obtain its boundary estimation. For certain families of graphs, we investigate the existence of modular edge-irregular total labelings and determine the precise values of the modular total edge-irregularity strength in order to prove the sharpness of the lower bound.

AB - Consider a simple graph G = (V, E) of size m with the vertex set V and the edge set E. A modular edge-irregular total k-labeling of a graph G is a labeling scheme for the vertices and edges with the labels 1, 2, …, k that allows the modular weights of any two different edges to be distinct, where the modular weight of an edge is the remainder of the division of the weight (i.e., the sum of the label of the edge itself and the labels of its two end vertices) by m. The maximal integer k, minimized over all modular edge-irregular total k-labelings of the graph G is called the modular total edge-irregularity strength. In the paper, we generalize the approach to edge-irregular evaluations, introduce the notion of the modular total edge-irregularity strength and obtain its boundary estimation. For certain families of graphs, we investigate the existence of modular edge-irregular total labelings and determine the precise values of the modular total edge-irregularity strength in order to prove the sharpness of the lower bound.

KW - circulant graph

KW - cycle

KW - modular edge-irregular labeling

KW - modular edge-irregularity strength

KW - modular total edge-irregularity strength

KW - n-sun

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U2 - 10.3934/math.20231287

DO - 10.3934/math.20231287

M3 - Article

AN - SCOPUS:85172263294

SN - 2473-6988

VL - 8

SP - 25249

EP - 25261

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 10

ER -