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On Distance Vertex Irregular Total k-Labeling Dian Eka Wijayanti; Noor Hidayat; Diari Indriati; Abdul Rouf Alghofari; Slamin
Science and Technology Indonesia Vol. 8 No. 3 (2023): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2023.8.3.479-485

Abstract

Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let σ:T∪S→1,2,· · · ,k, be a total k-labeling on H and wσ(x), be a weight of x∈T while using σ labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every x∈T has a different weight, then σ is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (Pr) and cycle (Cr) graphs. We establish a lower bound and then calculate the precise value of tdis(Pr) and tdis(Cr).
Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator Rio Satriyantara; Agus Suryanto; Noor Hidayat
The Journal of Experimental Life Science Vol. 8 No. 1 (2018)
Publisher : Postgraduate School, Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1177.162 KB) | DOI: 10.21776/ub.jels.2018.008.01.11

Abstract

In this paper, a fractional-order predator-prey model with prey refuge and additional food for predator is solved numerically. For that aim, the model is discretized using a piecewise constant arguments. The equilibrium points of the discrete fractional-order model are investigated. Numerical simulations are conducted to see the stability of each equilibrium point. The numerical simulations show that stability of the equilibrium points is dependent on the time step.Keywords: Additional Food, Fractional-Order, Predator-Prey, Prey Refuge.