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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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Multidesigns for the graph pair formed by the 6-cycle and 3-prism Yizhe Gao; Dan Roberts
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): 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.2020.8.1.10

Abstract

Given two graphs G and H, a (G,H)-multidecomposition of Kn is a partition of the edges of Kn into copies of G and H such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of (C6,Ċ6)-multidecomposition of Kn where C6 denotes a cycle of length 6 and C6 denotes the complement of C6. We also characterize the cardinalities of leaves and paddings of maximum (C6,Ċ6)-multipackings and minimum (C6,Ċ6)-multicoverings, respectively.
Sequence of maximal distance codes in graphs or other metric spaces Charles Delorme
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 2 (2013): 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.2013.1.2.5

Abstract

Given a subset C in a metric space E, its successor is the subset  s(C) of points at maximum distance from C in E. We study some properties of the sequence obtained by iterating this operation.  Graphs with their usual distance provide already typical examples.
On the spectrum of a class of distance-transitive graphs Seyed Morteza Mirafzal; Ali Zafari
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (2017): 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.2017.5.1.7

Abstract

Let $\Gamma=Cay(\mathbb{Z}_n, S_k)$ be the Cayley graph on the cyclic additive group $\mathbb{Z}_n$ $(n\geq 4),$  where  $S_1=\{1, n-1\}$, \dots , $S_k=S_ {k-1}\cup\{k, n-k\}$ are the inverse-closed subsets of $\mathbb{Z}_n-\{0\}$ for any $k\in \mathbb{N}$, $1\leq k\leq [\frac{n}{2}]-1$. In this paper,  we will show that $\chi(\Gamma) = \omega(\Gamma)=k+1$ if and only if $k+1|n$. Also, we will show that if $n$ is an even integer and $k=\frac{n}{2}-1$ then $Aut(\Gamma)\cong\mathbb{Z}_2 wr_{I} {Sym}(k+1)$ where $I=\{1, \dots , k+1\}$ and in this case, we show that $\Gamma$ is an  integral graph.
Maximum cycle packing using SPR-trees Christin Otto; Peter Recht
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (2019): 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.2019.7.1.11

Abstract

Let G = (V, E) be an undirected multigraph without loops. The maximum cycle packing problem is to find a collection Z *  = {C1, ..., Cs} of edge-disjoint cycles Ci subset G of maximum cardinality v(G). In general, this problem is NP-hard. An approximation algorithm for computing v(G) for 2-connected graphs is presented, which is based on splits of G. It essentially uses the representation of the 3-connected components of G by its SPR-tree. It is proved that for generalized series-parallel multigraphs the algorithm is optimal, i.e. it determines a maximum cycle packing Z *  in linear time.
The structure of the 3x + 1 problem Alf Kimms
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.14

Abstract

Paul Erdös said about the 3x+1 problem, "Mathematics is not yet ready for such problems". And he is seemingly right. Although we cannot solve this problem either, we provide some results about its structure. The so-called Collatz graph is iteratively transformed into a sequence of graphs by making use of some hidden structure information. It turns out that the transformation of graphs corresponds to a sequence of sets of numbers. It is shown that if the union of these number sets were equal to the set of integers greater than one, the famous Collatz conjecture would be true.
Vector weighted Stirling numbers and an application in graph theory Fahimeh Esmaeeli; Ahmad Erfanian; Madjid Mirzavaziri
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.20

Abstract

We introduce \textit{vector weighted Stirling numbers}, which are a generalization of ordinary Stirling numbers and restricted Stirling numbers. Some relations between vector weighted Stirling numbers and ordinary Stirling numbers and some of their applications are stated. Moreover, as an application of vector weighted Stirling numbers of the second kind in graph theory, we compute the number of maximal independent sets of different sizes in k-intersection graphs.
On distance labelings of 2-regular graphs Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.3

Abstract

Let G  be a graph with |V(G)| vertices and ψ :  V(G) → {1, 2, 3, ... , |V(G)|} be a bijective function. The weight of a vertex v ∈ V(G) under ψ is wψ(v) = ∑u ∈ N(v)ψ(u).  The function ψ is called a distance magic labeling of G, if wψ(v) is a constant for every v ∈ V(G).  The function ψ is called  an (a,d)-distance antimagic labeling of G, if the set of vertex weights is  a, a+d, a+2d, ... , a+(|V(G)|-1)d. A graph that admits a distance magic (resp. an (a,d)-distance antimagic) labeling is called  distance magic (resp.  (a,d)-distance antimagic).  In this paper, we characterize distance magic 2-regular graphs and   (a,d)-distance antimagic some classes of 2-regular graphs.
Roman domination in oriented trees Lyes Ouldrabah; Mostafa Blidia; Ahmed Bouchou
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.9

Abstract

Let D=(V,A) be a digraph of order n = |V|. A Roman dominating function of a digraph D is a function f : V  → {0,1,2} such that every vertex u for which f(u) = 0 has an in-neighbor v for which f(v) = 2. The weight of a Roman dominating function is the value f(V)=∑u∈V f(u). The minimum weight of a Roman dominating function of a digraph D is called the Roman domination number of D, denoted by γR(D). In this paper, we characterize oriented trees T satisfying γR(T)+Δ+(T) = n+1. 
Perfect codes in some products of graphs Samane Bakaein; Mostafa Tavakoli; Freydoon Rahbarnia
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.15

Abstract

A r-perfect code in a graph G = (V(G),E(G)) is a subset C of V(G) for which the balls of radius r centered at the vertices of C form a partition of V(G). In this paper, we study the existence of perfect codes in corona product and generalized hierarchical product of graphs where the cardinality of U is equal to one or two. Also, we give some examples as applications of our results.
A unique and novel graph matrix for efficient extraction of structural information of networks Sivakumar Karunakaran; Lavanya Selvaganesh
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (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.2021.9.1.4

Abstract

In this article, we propose a new type of square matrix associated with an undirected graph by trading off the natural embedded symmetry in them. The proposed matrix is defined using the neighbourhood sets of the vertices,  called as neighbourhood matrix NM(G).  The proposed matrix also exhibits a  bijection between the product of the two graph matrices, namely the adjacency matrix and the graph Laplacian. Alternatively, we define this matrix by using the breadth-first search traversals from every vertex, and the subgraph induced by the first two levels in the level decomposition from that vertex. The two levels in the level decomposition of the graph give us more information about the neighbours along with the neighbours-of-neighbour of a vertex. This insight is required and is found useful in studying the impact of broadcasting on social networks, in particular, and complex networks, in general. We establish several properties of NM(G). Additionally, we also show how to reconstruct a graph G, given an  NM(G). The proposed matrix also solves many graph-theoretic problems using less time complexity in comparison to the existing algorithms.

Page 20 of 39 | Total Record : 382

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