The total H-irregularity strength of triangular ladder graphs

Nisviasari, Rosanita; Dafik, Dafik; Agustin, Ika Hesti

doi:10.1088/1742-6596/1465/1/012026

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…The study of H-irregularity strength labeling has produced many findings from many researchers. It can be found in [4], [7], [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

The Reflexive H-Strength on Some Graphs

Sullystiawati,

Marsidi,

Putra

et al. 2024

CAUCHY

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Let G be a connected, simple, and undirected graph with a vertex set V(G) and an edge set E(G). The irregular reflexive -labeling is defined by the function and such that if and if , where max . The irregular reflexive labeling is called an -irregular reflexive -labeling of the graph if every two different sub graphs and isomorphic to it holds , where for the sub graph . The minimum for graph which has an -irregular reflexive -labelling is called the reflexive strength of the graph and denoted by . In this paper we determine the lower bound of the reflexive strength of some subgraphs, on , the sub graph on the sub graph on and the sub graph on .

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“…The study of H-irregularity strength labeling has produced many findings from many researchers. It can be found in [4], [7], [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

The Reflexive H-Strength on Some Graphs

Sullystiawati,

Marsidi,

Putra

et al. 2024

CAUCHY

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“…The smallest number of vertex weights needed to color the vertices of G such that no two adjacent vertices share the same color is called a local vertex irregular reflexive chromatic number, denoted by χ lrvs (G). Furthermore, the minimum k required such that χ lrvs (G) = χ(G) is called a local reflexive vertex color strength, denoted by lrvcs(G) [1]- [7], [11]- [12], [17]. In Fig.…”

Section: Introductionmentioning

confidence: 99%

On the Spatial Temporal Graph Neural Network Analysis Together with Local Vertex Irregular Reflexive Coloring for Time Series Forecasting on Passenger Density at Bus Station

Harliyuni,

Dafik,

Slamin

et al. 2023

Advances in Intelligent Systems Research

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The transportation problem that occurs in urban areas is how to meet the demand for the increasing number of trips and avoid traffic jams on the highway. In Indonesia, traffic density occurs during office hours, holidays, and national holidays. The solution to this problem is to use an effective public transportation service, one of which is the bus. Infrastructure for bus transportation includes roads, bridges, bus stops, and bus station. Bus station is one of the transportation systems that has the main function as a place to stop public transportation to pick up and drop passengers to the final destination of the trip. In this paper, we discuss the application of the concept of Spatial Temporal Graph Neural Network (STGNN) together with Local Vertex Irregular Reflexive Coloring (LVIRC) to analyze the passengers density anomaly of in bus station. The results shows that the use of the Spatial Temporal Graph Neural Network with Local Vertex Irregular Reflexive Coloring (LVIRC) are effective tools for forcasting the passengers density anomaly with the best model is generated by ANN-657 cascadeforwardnet, with a test MSE of 9.4982 ×10 −9 . Keywords: spatial temporal graph neural network • local vertex irregular reflexive coloring • time series forecasting • passengers density anomaly

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“…The minimum label of the largest label over all such irregular assignments is known as the irregularity strength of graph. The results of irregularity strength of graph can be seen in [1]- [5], [6,11,12]. Baca et al obtained the lower bound and the upper bound of total vertex irregularity strength on graph G, see [7].…”

Section: Introductionmentioning

confidence: 99%

On local vertex irregular reflexive coloring of graphs

Dafik

Koesoemawati

Agustin

et al. 2022

J. Phys.: Conf. Ser.

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Let χ(G) be a chromatic number of proper coloring on G. For an injection f : V (G) → {0, 2, . . . ; 2kυg } and f : E(G) → }1, 2, . . . , ke }, where k = max{ke , 2kχ } for kυ , ke are natural number. The associated weight of a vertex u, υ ∈ V (G) under f is w(u) = f(u) + ∑ uυ∈E(G)f(uυ). The function f is called a local vertex irregular reflexive k-labeling if every two adjacent vertices has distinct weight. When we assign each vertex of G with a color of the vertex weight w(uυ), thus we say the graph G admits a local vertex irregular reflexive coloring. The smallest number of vertex weights needed to color the vertices of G such that no two adjacent vertices share the same color is called a local vertex irregular reflexive chromatic number, denoted by χirvs (G). Furthermore, the minimum k required such that χlrvs (G) = χ(G) is called a local reflexive vertex color strength, denoted by lrvcs(G). In this paper, we will obtain the lrvcs(G) and characterize the existence of a graph with given its local reflexive vertex color strength.

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The total H-irregularity strength of triangular ladder graphs

Cited by 3 publications

References 7 publications

The Reflexive H-Strength on Some Graphs

The Reflexive H-Strength on Some Graphs

On the Spatial Temporal Graph Neural Network Analysis Together with Local Vertex Irregular Reflexive Coloring for Time Series Forecasting on Passenger Density at Bus Station

On local vertex irregular reflexive coloring of graphs

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