On cycle-irregularity strength of ladders and fan graphs

Ashraf, Faraha; Bača, Martin; Semaničová-Feňovčíková, Andrea; Saputro, Suhadi Wido

doi:10.5614/ejgta.2020.8.1.13

Cited by 3 publications

(2 citation statements)

References 14 publications

(17 reference statements)

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“…They discovered that for any graph, the irregularity strength sðGÞ: , which is the lowest possible value k for which G constitutes an irregular assignment with label at most k, is extremely difficult to find. In recent times, motivated by this particular concept, many researchers are having specific interest for these types of irregular labeling and have found the irregularity strength for some graphs [5][6][7][8][9][10]. Shabbir et al [11] have proved their exact values of the strength of total vertex (edge) irregularities of a randomly convex unions of (3,6)-fullerene graphs.…”

Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Certain Graphs

Emilet,

Paul,

Jayagopal

et al. 2024

Mathematical Problems in Engineering

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The edge k-labeling ψ of G is defined by a mapping from EG to a set of integers 1,2,…,k, where the integer weight assigned to the vertex x∈VG is given as wψx=∑ψxy, such that the sum is taken over every vertex of y∈VG that is adjacent to x and the integer weights of adjacent vertices must be distinct for all vertices with x≠y. An irregular assignment of G using atmost k labels which is considered to be a minimum k is defined as irregularity strength of a graph G and can be denoted as sG. There are also further works on familiar irregular assignments, such as edge irregular labelings, vertex irregular total labelings, edge irregular total labelings, and face irregular entire k-labelings of plane graphs. A plane graph can be defined as a graph that is embedded in the plane in which no two lines will be intersected. In a plane graph the number of regions present are called faces and we denote it as F. The concept of total face irregularity strength is defined by the motivation of irregular networks and entire irregular face k-labeling. In our paper, we have obtained a minimum bound for the total face irregularity strength of two-connected plane graphs like cycle-of-ladder, C-necklace graph, P-necklace graph, sibling tree, and triangular graph.

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Section: Introductionmentioning

confidence: 99%

Total Face Irregularity Strength of Certain Graphs

Emilet,

Paul,

Jayagopal

et al. 2024

Mathematical Problems in Engineering

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“…The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of the graph G, tes(G). Some results on the total edge irregularity strength can be found in [1], [3], [4], [8], [9], [13], [14], [15] and [19].…”

Section: Introductionmentioning

confidence: 99%

On reflexive edge strength of generalized prism graphs

Irfan

Bača

Semaničová-Feňovčíková

2022

EJGTA

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Let G be a connected, simple and undirected graph. The assignments {0, 2, . . . , 2k v } to the vertices and {1, 2, . . . , k e } to the edges of graph G are called total k-labelings, where k = max{k e , 2k v }. The total k-labeling is called an reflexive edge irregular k-labeling of the graph G, if for every two different edges xy and x y of G, one has wt(xy) = f v (x) + f e (xy) + f v (y) = wt(x y ) = f v (x ) + f e (x y ) + f v (y ). The minimum k for which the graph G has an reflexive edge irregular k-labeling is called the reflexive edge strength of G. In this paper we investigate the exact value of reflexive edge strength for generalized prism graphs.

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On H-irregularity strength of cycles and diamond graphs

Labane

Bouchemakh

Semaničová-Feňovčíková

2021

Discrete Math. Algorithm. Appl.

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A simple graph [Formula: see text] admits an [Formula: see text]-covering if every edge in [Formula: see text] belongs to at least one subgraph of [Formula: see text] isomorphic to a given graph [Formula: see text]. The graph [Formula: see text] admits an [Formula: see text]-irregular total[Formula: see text]-labeling [Formula: see text] if [Formula: see text] admits an [Formula: see text]-covering and for every two different subgraphs [Formula: see text] and [Formula: see text] isomorphic to [Formula: see text], there is [Formula: see text], where [Formula: see text] is the associated [Formula: see text]-weight. The total[Formula: see text]-irregularity strength of [Formula: see text] is [Formula: see text]. In this paper, we give the exact values of [Formula: see text], where [Formula: see text]. For the versions edge and vertex [Formula: see text]-irregularity strength [Formula: see text] and [Formula: see text], respectively, we determine the exact values of [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is the diamond graph.

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On cycle-irregularity strength of ladders and fan graphs

Abstract: A simple graph G = (

Cited by 3 publications

References 14 publications

Total Face Irregularity Strength of Certain Graphs

Total Face Irregularity Strength of Certain Graphs

On reflexive edge strength of generalized prism graphs

On H-irregularity strength of cycles and diamond graphs

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