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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 25 Documents
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Search results for , issue "Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications" : 25 Documents clear
Harmonious graphs from α-trees Christian Barrientos; Sarah Minion
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.9

Abstract

Two of the most studied graph labelings are the types of harmonious and graceful. A harmonious labeling of a graph of size m and order n, is an injective assignment of nonnegative integers smaller than m, such that the weights of the edges, which are defined as the sum of the labels of the end-vertices, are distinct consecutive integers after reducing modulo m. When n = m + 1, exactly two vertices of the graph have the same label. An α-labeling of a tree of size m is a bijective assignment of nonnegative integers, not larger than m, such that the labels on one stable set are smaller than the labels on the other stable set, and the weights of the edges, which are defined as the absolute difference of the labels of the end-vertices, are all distinct; this is the most restrictive type of graceful labeling. Even when these labelings are significantly different in their definitions of the weight, for certain kinds of graphs, there is a deep connection between harmonious and α-labelings. We present new families of harmoniously labeled graphs built on α-labeled trees. Among these new results there are three families of trees, the kth power of the path Pn, the join of a graph G and tK1 where G is a graph that admits a more restrictive type of harmonious labeling and its order is different of its size by at most one unit. We also prove the existence of two families of disconnected harmonius graphs: Kn, m ∪ K1, m − 1 and G ∪ T, where G is a unicyclic graph and T is a tree built with α-trees. In addition, we show that almost all trees admit a harmonious labeling.
On hamiltonicity of 1-tough triangle-free graphs Wei Zheng; Hajo Broersma; Ligong Wang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.15

Abstract

Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in general, and even not for triangle-free graphs. We present two classes of triangle-free graphs for which the reverse statement holds, i.e., for which hamiltonicity and 1-toughness are equivalent. Our two main results give partial answers to two conjectures due to Nikoghosyan.
Embedding complete multi-partite graphs into Cartesian product of paths and cycles R. Sundara Rajan; A. Arul Shantrinal; T.M. Rajalaxmi; Jianxi Fan; Weibei Fan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.21

Abstract

Graph embedding is a powerful method in parallel computing that maps a guest network G into a host network H. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion, and the wirelength. In this manuscript, we obtain the wirelength (exact and minimum) of embedding complete multi-partite graphs into Cartesian product of paths and/or cycles, which include n-cube, n-dimensional mesh (grid), n-dimensional cylinder, and n-dimensional torus, etc., as the subfamilies.
On the k-rainbow domination in graphs with bounded tree-width M. Alambardar Meybodi; M. R. Hooshmandasl; P. Sharifani; Ali Shakiba
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.4

Abstract

Given a positive integer k and a graph G = (V, E), a function f from V to the power set of Ik is called a k-rainbow function if for each vertex v ∈ V, f(v)=∅ implies ∪u ∈ N(v)f(u)=Ik where N(v) is the set of all neighbors of vertex v and Ik = {1, …, k}. Finding a k-rainbow function of minimum weight of ∑v ∈ V|f(v)|, which is called the k-rainbow domination problem, is known to be NP-complete for arbitrary graphs and values of k. In this paper, we propose a dynamic programming algorithm to solve the k-rainbow domination problem for graphs with bounded tree-width tw in ????((2k + 1+1)twn) time, where G has n vertices. Moreover, we also show that the same approach is applicable to solve the weighted k-rainbow domination problem with the same complexity. Therefore, both problems of k-rainbow and weighted k-rainbow domination belong to the class FPT, or fixed parameter tractable, with respect to tree-width. In addition to formally showing the correctness of our algorithms, we also implemented these algorithms to illustrate some examples.
All missing Ramsey numbers for trees versus the four-page book Roland Lortz; Ingrid Mengersen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.10

Abstract

For the Ramsey number r(Tn, Bm), where Tn denotes a tree of order n and Bm denotes the m-page book K2 + bar(K)m, it is known that r(Tn, Bm)=2n − 1 if n ≥ 3m − 3. In case of n < 3m − 3, r(Tn, Bm) has not been completely evaluated except for m ≤ 3. Here we determine the missing values of r(Tn, B4). Our results close one gap in the table of the Ramsey numbers r(Tn, G) for all trees Tn and all connected graphs G of order six.
On strict-double-bound numbers of graphs and cut sets Kazutaka Ikeda; Kenjiro Ogawa; Satoshi Tagusari; Shin-ichiro Tashiro; Morimasa Tsuchiya
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.16

Abstract

For a poset P=(X,≤P), the strict-double-bound graph of P is the graph sDB(P) on V(sDB(P))=X for which vertices u and v of sDB(P) are adjacent if and only if u ≠ v and there exist elements x,y ∈ X distinct from u and v such that x ≤P u ≤P y and x ≤P v ≤P y. The strict-double-bound number ζ(G) of a graph G is defined as min{ n ; sDB(P) ≅ G ∪ Ǩn {for  some poset P}. We obtain an upper bound of strict-double-bound numbers of graphs with a cut-set generating a complete subgraph. We also estimate upper bounds of strict-double-bound numbers of chordal graphs.
On d-Fibonacci digraphs C. Dalfó; M.A. Fiol
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.22

Abstract

The d-Fibonacci digraphs F(d, k), introduced here, have the number of vertices following some generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their nice properties. For instance, F(d, k) has diameter d + k − 2 and is semi-pancyclic; that is, it has a cycle of every length between 1 and ℓ, with ℓ ∈ {2k − 2, 2k − 1}. Moreover, it turns out that several other numbers of F(d, k) (of closed l-walks, classes of vertices, etc.) also follow the same linear recurrences as the numbers of vertices of the d-Fibonacci digraphs.
The integer-antimagic spectra of Hamiltonian graphs Ugur Odabasi; Dan Roberts; Richard M. Low
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.5

Abstract

Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f : E(G)→A ∖ {0A} such that the induced vertex labeling f+(v)=∑{u, v}∈E(G)f({u, v}) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM (G)={k : G is ℤk-antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.
Complete bipartite graph is a totally irregular total graph Meilin I. Tilukay; Pranaya D. M. Taihuttu; A. N. M. Salman; Francis Y. Rumlawang; Zeth A. Leleury
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.11

Abstract

A graph G is called a totally irregular total k-graph if it has a totally irregular total k-labeling λ : V ∪ E→ 1, 2, ... , k, that is a total labeling such that for any pair of different vertices x and y of G, their weights wt(x) and wt(y) are distinct, and for any pair of different edges e and f of G, their weights wt(e) and wt(f) are distinct. The minimum value k under labeling λ is called the total irregularity strength of G, denoted by ts(G). For special cases of a complete bipartite graph Km, n, the ts(K1, n) and the ts(Kn, n) are already determined for any positive integer n. Completing the results, this paper deals with the total irregularity strength of complete bipartite graph Km, n for any positive integer m and n.
On maximum packings of λ-fold complete 3-uniform hypergraphs with triple-hyperstars of size 4 Amber Armstrong; Ryan C. Bunge; William Duncan; Saad I. El-Zanati; Kristin Koe; Rachel Stutzman
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): 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.2021.9.2.17

Abstract

A symmetric triple-hyperstar is a connected, 3-uniform hypergraph where, for some edge {a, b, c}, vertices a, b, and c all have degree k > 1 and all other edges contain exactly 2 vertices of degree 1. Let H denote the symmetric triple-hyperstar with 4 edges and, for positive integers λ and v, let λKv(3) denote the λ-fold complete 3-uniform hypergraph on v vertices. We find maximum packings of λKv(3) with copies of H.

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