On Distance Irregular Labelling of Graphs

Slamin, .

doi:10.17654/ms102050919

Cited by 24 publications

(32 citation statements)

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“…The notion of non-inclusive distance vertex irregular labelings was intoduced in 2017 by Slamin [13]. Meanwhile, Bača et al [3] developed inclusive distance vertex irregular labelings one year later as a variation of the non-inclusive irregularity strength of graphs.…”

Section: Introductionmentioning

confidence: 99%

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Non-inclusive and inclusive distance irregularity strength for the join product of graphs

Susanto

Wijaya

Sudarsana

et al. 2022

EJGTA

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A function φ : V (G) → {1, 2, . . . , k} of a simple graph G is said to be a non-inclusive distance vertex irregular k-labeling of G if the sums of labels of vertices in the open neighborhood of every vertex are distinct and is said to be an inclusive distance vertex irregular k-labeling of G if the sums of labels of vertices in the closed neighborhood of each vertex are different. The minimum k for which G has a non-inclusive (resp. an inclusive) distance vertex irregular k-labeling is called a non-inclusive (resp. an inclusive) distance irregularity strength and is denoted by dis(G) (resp. by dis(G)). In this paper, the non-inclusive and inclusive distance irregularity strength for the join product graphs are investigated.

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Section: Introductionmentioning

confidence: 99%

“…A number of research results on non-inclusive and inclusive d-distance irregularity strengths have been found as seen in [3,4,11,13,14,15,16,17] when d = 1 and in [5,18] when d > 1.…”

Section: Introductionmentioning

confidence: 99%

Non-inclusive and inclusive distance irregularity strength for the join product of graphs

Susanto

Wijaya

Sudarsana

et al. 2022

EJGTA

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“…Motivated by distance labeling that is introduced by Miller et al [5] and irregular assignment by Chartrand et al [3], Slamin [6] introduced a new variation of vertex labeling, that is called distance irregular labeling. It is a vertex labeling f : VðGÞ !…”

Section: Introductionmentioning

confidence: 99%

On inclusive d-distance irregularity strength on triangular ladder graph and path

Utami

Sugeng

Utama

2020

AKCE International Journal of Graphs and Combinatorics

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The length of a shortest path between two vertices u and v in a simple and connected graph G, denoted by d(u, v), is called the distance of u and v. An inclusive vertex irregular d-distance labeling is a labeling defined as k : VðGÞ ! f1, :::, kg such that the vertex weight, that is wtðvÞ ¼ kðvÞ þ P fu:1 dðu, vÞ dg kðuÞ, are all distinct. The minimal value of the largest label used over all such labeling of graph G, denoted by dis 0 d ðGÞ, is defined as inclusive d-distance irregularity strength of G. Others studies have concluded the lower bound value of dis 0 1 ðGÞ and the value of dis 0 1 ðL n Þ: In this paper, we generalize the lower bound value of dis 0 d ðGÞ for d ! 2: We used the lower bound value of dis 0 d ðGÞ and the previous result of dis 0 1 ðL n Þ to investigate the value of dis 0 2 ðL n Þ: As a result, we found the exact values of dis 0 2 ðL n Þ for the cases n 0, 3, 4, 5, 8 ðmod9Þ, n ¼ 7, and the value of the upper bound of dis 0 2 ðL n Þ for other n. We also found the relation of the value of dis 0 d ðL n Þ and the value of dis 0 2d ðP 2n Þ: Further investigation on path brought us to conclude the exact value of dis 0 2 ðP n Þ, dis 0 3 ðP n Þ and dis 0 4 ðP n Þ for some n.

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“…The notion of sigma coloring is related to the vertex colorings/labellings discussed in Refs. [1], [8], [11]. These colorings/labellings also use the sum of the colors/labels of a vertex's neighbors.…”

Section: Introductionmentioning

confidence: 99%

Sigma Coloring and Edge Deletions

Garciano

Marcelo

Ruiz

et al. 2020

Journal of Information Processing

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A vertex coloring c : V(G) → N of a non-trivial graph G is called a sigma coloring if σ(u) σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G) − σ(G − e) in general as well as in restricted scenarios; here, G − e is the graph obtained by deleting an edge e from G. Furthermore, we study the sigma chromatic number of graphs obtained via multiple edge deletions in complete graphs by considering the complements of paths and cycles.

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On Distance Irregular Labelling of Graphs

Cited by 24 publications

References 0 publications

Non-inclusive and inclusive distance irregularity strength for the join product of graphs

Non-inclusive and inclusive distance irregularity strength for the join product of graphs

On inclusive d-distance irregularity strength on triangular ladder graph and path

Sigma Coloring and Edge Deletions

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