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INDONESIA
Electronic Journal of Graph Theory and Applications (EJGTA)
Published by Indonesian Combinatorial Society
ISSN : 23382287     EISSN : -     DOI : -
Core Subject : Engineering,
Electrical & Electronics Engineering
The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society (InaCombS), Graph Theory and Applications (GTA) Research Group - The University of Newcastle - Australia, and Faculty of Mathematics and Natural Sciences - Institut Teknologi Bandung (ITB) Indonesia. Subscription to EJGTA is free. Full-text access to all papers is available for free. All research articles as well as surveys and articles of more general interest are welcome. All papers will be refereed in the normal manner of mathematical journals to maintain the highest standards. This journal is sponsored by CARMA (Computer-Assisted Research Mathematics and its Applications) Priority Research Centre - The University of Newcastle - Australia, and Study Program of Information System- University of Jember - Indonesia.
Arjuna Subject : -
Articles 15 Documents
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Search results for , issue "Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications" : 15 Documents clear
A new look at the concept of domination in hypergraphs Divya, P.M.; Ramakrishnan, T.V.; Arumugam, Subramanian
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.3

Abstract

In this paper we propose a new definition of domination in hypergraphs in such a way that when restricted to graphs it is the usual domination in graphs. Let H = (V,E) be a hypergraph. A subset S of V is called a dominating set of H if for every vertex v in V -S, there exists an edge e ∈ E such that v ∈ e and e-{v}⊆ S. The minimum cardinality of a dominating set of H is called the domination number of H and is denoted by γ(H). We determine the domination number for several classes of uniform hypergraphs. We characterise minimal dominating sets and introduce the concept of independence and irredundance leading to domination chain in hypergraphs.
Embedding partial 3-star designs Noble, Matt; Nochumson, Shayne
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/jgta.2024.12.2.9

Abstract

Define a 3-star decomposition of Kn as being a collection of subgraphs, each isomorphic to K1,3, with the property that each edge of Kn appears in exactly one of the subgraphs. A partial 3-star decomposition is similarly defined except each edge appears in at most one of the subgraphs. In this work, it is shown that any partial 3-star decomposition of Kn can be embedded into a decomposition of Kn+s where s ≤ 4. Furthermore, we determine, for any maximal partial 3-star decomposition P of Kn, the minimum s ∈{1,2,3,4} such that P can be embedded into a decomposition of Kn+s.
On the incidence graph of circular spaces Sorgun, Sezer; Ertaş, Ali Gökhan; Günaltılı, İbrahim
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.15

Abstract

A configuration of the triple (P,L,I) is an incidence relation which has the properties "any two points are incident with at most one line" and "any two lines are incident with at most one point". In projective geometry, bipartite graphs can be used as an incidence model between the points and lines of a configuration. The graphs associated with a space are a good tool for understanding the topological and geometric properties of space in abstract systems. In this paper we focus on the incidence graph of circular space and obtain its properties in terms of some pure graph invariants. We also characterize it in terms of the graphs associated with other spaces in the literature.
Magic labeling on graphs with ascending subgraph decomposition Pancahayani, Sigit; Simanjuntak, Rinovia; Uttunggadewa, Saladin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.4

Abstract

Let t and q be positive integers that satisfy C(t + 1,2) ≤ q < C(t + 2,2) and let G be a simple and finite graph of size q. G is said to have ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H1,H2,…,Ht without isolated vertices such that Hi is isomorphic to a proper subgraph of Hi+1 for 1 ≤ i ≤ t - 1, where {E(H1),…,E(Ht)} is a partition of E(G). A graph that admits an ascending subgraph decomposition is called an ASD graph.In this paper, we introduce a new type of magic labeling based on the notion of ASD. Let G be an ASD graph and f : V (G) ∪E(G) →{1,2,…,|V (G)| + |E(G)|} be a bijection. The weight of a subgraph Hi (1 ≤ i ≤ n) is w(Hi) = ∑ v∈V (Hi)f(v) + ∑ e∈E(Hi)f(e). If the weight of each ascending subgraph is constant, say w(Hi) = k, ∀ 1 ≤ i ≤ t, then f is called an ASD-magic labeling of G and G is called an ASD-magic graph. We present general properties of ASD-magic graphs and characterize certain classes of them.
Computational complexity of the police officer patrol problem on weighted digraphs Tomisawa, Masaki; Tohyama, Hiroaki
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.10

Abstract

A vertex cover of a graph is a set of vertices that includes at least one endpoint of every edge of the graph and can be regarded as the placement of police officers or fixed surveillance cameras so that each street of a neighborhood represented by the graph can be confirmed visually without moving from their position. Given a graph G and a natural number k, the vertex cover problem is the problem of deciding whether there exists a vertex cover in G of size at most k. The vertex cover problem is one of Karp’s 21 NP-complete problems.Recently, we introduced an edge routing problem that a single police officer must confirm all the streets. The officer is allowed to move, but can confirm any street visually from an incident intersection without traversing it. We showed that the problem of deciding whether there exists a patrol route for a given mixed graph in which each edge is either traversed exactly once or confirmed visually is NP-complete. In this paper, we show that the police officer patrol problem remains NP-complete even if given graphs are weighted digraphs.

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