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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 382 Documents
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The dominant edge metric dimension of graphs Mostafa Tavakoli; Meysam Korivand; Ahmad Erfanian; Gholamreza Abrishami; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.16

Abstract

For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e′ of G, the edge metric S-representation of e′=ab is the vector rGe(e′|S)=(dG(e′,v1),…,dG(e′,vk)) , where dG(e′,vi)=min{dG(a, vi),dG(b, vi)}. A dominant edge metric generator for G is a vertex cover S of G such that the edges of G have pairwise different edge metric S-representations. A dominant edge metric generator of smallest size of G is called a dominant edge metric basis for G. The size of a dominant edge metric basis of G is denoted by Ddime(G) and is called the dominant edge metric dimension. In this paper, the concept of dominant edge metric dimension (DEMD for short) is introduced and its basic properties are studied. Moreover, NP-hardness of computing DEMD of connected graphs is proved. Furthermore, this invariant is investigated under some graph operations at the end of the paper.
Decomposing K18n and K18n + 1 into connected unicyclic graphs with 9 edges Grace Aspenson; Dustin Baker; Bryan Freyberg; Coy Schwieder
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.22

Abstract

Other than C9 there are 239 connected unicyclic graphs with exactly 9 edges. We use established graph labeling results to prove that every one of them decomposes the complete graph Kn if n ≡ 0 or 1 (mod 18).
On (F, H)-simultaneously-magic labelings of graphs Yeva Fadhilah Ashari; A.N.M. Salman; Rinovia Simanjuntak; Andrea Semaničová-Feňovčíková; Martin Baca
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.5

Abstract

A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorphic to H. In this case, G is called H-magic if there exists a bijective function f : V ∪ E → {1, 2, …, |V|+|E|}, such that for every subgraph H′ of G isomorphic to H, wtf(H′) =  Σv ∈ V(H′)f(v)+ Σe ∈ E(H′)f(e) is constant. Moreover, G is called H-supermagic if f : V(G)→{1, 2, …, |V|}. This paper generalizes the previous labeling by introducing the (F, H)-sim-(super) magic labeling. A graph admitting an F-covering and an H-covering is called (F, H)-sim-(super) magic if there exists a function f that is F-(super)magic and H-(super)magic at the same time. We consider such labelings for two product graphs: the join product and the Cartesian product. In particular, we establish a sufficient condition for the join product G + H to be (K2 + H, 2K2 + H)-sim-supermagic and show that the Cartesian product G × K2 is (C4, H)-sim-supermagic, for H isomorphic to a ladder or an even cycle. Moreover, we also present a connection between an α-labeling of a tree T and a (C4, C6)-sim-supermagic labeling of the Cartesian product T × K2.
On the inverse graph of a finite group and its rainbow connection number Rian Febrian Umbara; A.N.M. Salman; Pritta Etriana Putri
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.11

Abstract

A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called the rainbow connection number of G. Let (Γ, *) be a finite group with TΓ = {t ∈ Γ|t ≠ t−1}. The inverse graph of Γ, denoted by IG(Γ), is a graph whose vertex set is Γ and two distinct vertices, u and v, are adjacent if u * v ∈ TΓ or v * u ∈ TΓ. In this paper, we determine the necessary and sufficient conditions for the inverse graph of a finite group to be connected. We show that the inverse graph of a finite group is connected if and only if the group has a set of generators whose all elements are non-self-invertible. We also determine the rainbow connection numbers of the inverse graphs of finite groups.
Total distance vertex irregularity strength of some corona product graphs Dian Eka Wijayanti; Noor Hidayat; Diari Indriati; Abdul Rouf Alghofari; Slamin Slamin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.17

Abstract

A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V(G)∪E(G)→{1, 2, …, k} such that for every pair vertices u, v ∈ V(G) and u ≠ v, the weights of u and v are distinct. The weight of vertex v ∈ V(G) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v. The total distance vertex irregularity strength of G (denoted by tdis(G)) is the minimum of k for which G has a distance vertex irregular total k-labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.
The matching book embeddings of pseudo-Halin graphs Zeling Shao; Yanling Hu; Huiru Geng; Zhiguo Li
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.23

Abstract

The book embedding of a graph G is to arrange the set of points of the graph on a line (spine) and embed the edges on the half-plane bounded by the spine so that the edges in the same page do not intersect with each other. If the maximum degree of vertices in each page is 1, the book embedding is matching book embedding. The matching book thickness of G is the minimum number n that G can be matching book embedded in n-page. In this paper, the matching book thickness of pseudo-Halin graphs is determined.
γ-Paired dominating graphs of lollipop, umbrella and coconut graphs Pannawat Eakawinrujee; Nantapath Trakultraipruk
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.6

Abstract

A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set D is a γpr(G)-set if |D|=γpr(G). The γ-paired dominating graph PDγ(G) of G is the graph whose vertex set is the set of all γpr(G)-sets, and two γpr(G)-sets D1 and D2 are adjacent in PDγ(G) if D2 = (D1 \ {u}) ∪ {v} for some u ∈ D1 and v ∉ D1. This paper determines the paired domination numbers of lollipop graphs, umbrella graphs, and coconut graphs. We also consider the γ-paired dominating graphs of those three graphs.
On Ramsey (C4, K1, n)-minimal graphs Hilda Assiyatun; Maya Nabila; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.12

Abstract

Let F, G and H be any simple graphs. The notation F → (G, H) means for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. If F → (G, H), then graph F is called a Ramsey graph for (G, H). Additionally, if the graph F satisfies that F − e ↛ (G, H) for any edge e of F, then graph F is called a Ramsey (G, H)-minimal. The set of all Ramsey (G, H)-minimal graphs is denoted by ℛ(G, H). In this paper, we construct a new class of Ramsey (C4, K1, n)-minimal graphs. 
Total coloring conjecture on certain classes of product graphs Kanagasabapathi Somasundaram; Jayabalan Geetha; Radhakrishnan Vignesh
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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.2023.11.1.18

Abstract

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G, denoted by χ″(G), is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ(G)+1 ≤ χ″(G)≤Δ(G)+2, where Δ(G) is the maximum degree of G. In this paper, we prove the Behzad and Vizing conjecture for Indu - Bala product graph, Skew and Converse Skew product graph, Cover product graph, Clique cover product graph and Comb product graph.
On decompositions of complete graphs into unicyclic disconnected bipartite graphs on nine edges Alan Bonhert; Luke Branson; Patrick Joseph Otto
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): 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

Abstract

We use Rosa-type labelings to decompose complete graphs into unicyclic, disconnected, bipartite graphs on nine edges – namely, those featuring cyclic component C4, C6, or C8. For any such graph H, we prove there exists an H-design of K18k + 1 and K18k for all positive integers k.

Page 31 of 39 | Total Record : 382

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