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A Simple Modelling of Microscopic Epidemic Process with Two Vaccine Doses on a Synthesized Human Interaction Network Seprianus; Nuraini, Nuning; Saputro, Suhadi Wido
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.6

Abstract

In this study, we illustrate the incorporation of two vaccine doses into a discrete SIR model to aid in the decision-making process for optimal vaccination strategies. We present a basic model of a human interaction network synthesized to depict social contacts within a population, taking into account the number of connections and the level of interaction among individuals. Under a limited number of available vaccine doses, we explore various vaccination scenarios considering factors such as the distribution of vaccines, the proportion of vaccinated individuals, and the timing of vaccination commencement. Our research demonstrates that the most effective vaccination strategy, which focuses on re-characterized hubs or redefining the individual who has high connectivity, will cover fewer individuals and result in the smallest total number of infected individuals.
On Ramsey numbers for trees versus fans of even order Sherlin, Intan; Saputro, Suhadi Wido; Baskoro, Edy Tri; Oktariani, Finny
Indonesian Journal of Combinatorics Vol 8, No 1 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.1.2

Abstract

Given two graphs G and H. The graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or F̅ contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel Wm is a graph consisting one dominating vertex and m other vertices forming a cycle. A fan graph F1,m is a graph formed from a wheel Wm by removing one cycle-edge. In this paper, we consider the graph Ramsey number R(Tn,F1,m) of a tree Tn versus a fan F1,m. The study of R(Tn,F1,m) has been initiated by Li et. al. (2016) where Tn is a star, and continued by Sherlin et. al. (2023) for Tn which is not a star and fan F1,m with even m ≤ 8. This paper will give the graph Ramsey numbers R(Tn,F1,m) for odd m ≤ 8.
Partition dimension of disjoint union of complete bipartite graphs Haryeni, Debi Oktia; Baskoro, Edy Tri; Saputro, Suhadi Wido
Desimal: Jurnal Matematika Vol. 4 No. 2 (2021): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v4i2.10190

Abstract

For any (not necessary connected) graph $G(V,E)$ and $A\subseteq V(G)$, the distance of a vertex $x\in V(G)$ and $A$ is $d(x,A)=\min\{d(x,a): a\in A\}$. A subset of vertices $A$ resolves two vertices $x,y \in V(G)$ if $d(x,A)\neq d(y,A)$. For an ordered partition $\Lambda=\{A_1, A_2,\ldots, A_k\}$ of $V(G)$, if all $d(x,A_i)<\infty$ for all $x\in V(G)$, then the representation of $x$ under $\Lambda$ is $r(x|\Lambda)=(d(x,A_1), d(x,A_2), \ldots, d(x,A_k))$. Such a partition $\Lambda$ is a resolving partition of $G$ if every two distinct vertices $x,y\in V(G)$ are resolved by $A_i$ for some $i\in [1,k]$. The smallest cardinality of a resolving partition $\Lambda$ is called a partition dimension of $G$ and denoted by $pd(G)$ or $pdd(G)$ for connected or disconnected $G$, respectively. If $G$ have no resolving partition, then $pdd(G)=\infty$. In this paper, we studied the partition dimension of disjoint union of complete bipartite graph, namely $tK_{m,n}$ where $t\geq 1$ and $m\geq n\geq 2$. We gave the necessary condition such that the partition dimension of $tK_{m,n}$ are finite. Furthermore, we also derived the necessary and sufficient conditions such that $pdd(tK_{m,n})$ is either equal to $m$ or $m+1$.
On ON LOCATING-DOMINATING SET OF THE CARTESIAN PRODUCT OF COMPLETE BIPARTITE GRAPHS AND A PATH OF ORDER TWO Saputro, Suhadi Wido; As-Shidiq, Ikhsan Rizqi Az-Zukruf
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.208-215.2025

Abstract

A set D is called as a locating-dominating set of a graph G if D is a dominating set of G such that every vertex outside D is uniquely identified by its neighbourhood within D. The locating-dominating number of G is the minimum cardinality of all locating-dominating sets of G. In this paper, we consider a Cartesian product graphs between a complete bipartite graphs Km1,m2 and a path of order two P2, denoted by Km1,m2P2. In particular, we determine the locating-dominating number of Km1,m2P2 for any values m1 and m2 at least 2.