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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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Orientable Z_n-distance magic labeling of the Cartesian product of many cycles Bryan Freyberg; Melissa Keranen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (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.2017.5.2.11

Abstract

The following generalization of distance magic graphs was introduced in [2]. A directed Z_n-distance magic labeling of an oriented graph $\overrightarrow{G}=(V,A)$ of order n is a bijection $\overrightarrow{\ell}\colon V \rightarrow Z_n$ with the property that there is a $\mu \in Z_n$ (called the magic constant) such that w(x)= \sum_{y\in N_{G}^{+}(x)} \overrightarrow{\ell}(y) - \sum_{y\in N_{G}^{-}(x)} \overrightarrow{\ell}(y)= \mu$ for every x \in V(G). If for a graph G there exists an orientation $\overrightarrow{G}$ such that there is a directed Z_n-distance magic labeling $\overrightarrow{\ell}$ for $\overrightarrow{G}$, we say that G is orientable Z_n-distance magic and the directed Z_n-distance magic labeling $\overrightarrow{\ell}$ we call an orientable Z_n-distance magic labeling. In this paper, we find orientable Z_n-distance magic labelings of the Cartesian product of cycles. In addition, we show that even-ordered hypercubes are orientable Z_n-distance magic.
Cycle decompositions and constructive characterizations Irene Heinrich; Manuel Streicher
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (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.2019.7.2.15

Abstract

Decomposing an Eulerian graph into a minimum respectively maximum number of edge disjoint cycles is an NP-complete problem. We prove that an Eulerian graph decomposes into a unique number of cycles if and only if it does not contain two edge disjoint cycles sharing three or more vertices. To this end, we discuss the interplay of three binary graph operators leading to novel constructive characterizations of two subclasses of Eulerian graphs. This enables us to present a polynomial-time algorithm which decides whether the number of cycles in a cycle decomposition of a given Eulerian graph is unique.
The Manhattan product of digraphs Francesc Comellas; Cristina Dalfo; Miquel Àngel Fiol
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 1 (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.2013.1.1.2

Abstract

We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants.
Notes on the combinatorial game: graph Nim Richard M. Low; W.H. Chan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): 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.2016.4.2.7

Abstract

The combinatorial game of Nim can be played on graphs. Over the years, various Nim-like games on graphs have been proposed and studied by N.J. Calkin et al., L.A. Erickson and M. Fukuyama. In this paper, we focus on the version of Nim played on graphs which was introduced by N.J. Calkin et al.: Two players alternate turns, each time choosing a vertex $v$ of a finite graph and removing any number $(\geq 1)$ of edges incident to $v$. The player who cannot make a move loses the game. Here, we analyze Graph Nim for various classes of graphs and also compute some Grundy-values.
On friendly index sets of k-galaxies S-M Lee; Richard M. Low; H.K. Ng; Y-C Wang
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.2019.7.1.1

Abstract

Let G = (V, E) be a graph. A vertex labeling f : V → Z2 induces an edge labeling f *  : E → Z2 defined by f * (xy) = f(x) + f(y), for each edge xy ∈ E. For i ∈ Z2, let vf(i) = ∣{v ∈ V : f(v) = i}∣ and ef(i) = ∣{e ∈ E : f * (e) = i}∣. We say that f is friendly if ∣vf(1) − vf(0)∣ ≤ 1. The friendly index set of G, denoted by FI(G), is defined as FI(G) = ∣ef(1) − ef(0)∣ :  vertex labeling f is friendly. A k-galaxy is a disjoint union of k stars. In this paper, we establish the friendly index sets for various classes of k-galaxies.
The partition dimension of a subdivision of a homogeneous firecracker Amrullah Amrullah
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (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.2020.8.2.20

Abstract

Finding the partition dimension of a graph is one of the interesting (and uncompletely solved) problems of graph theory. For instance, the values of the partition dimensions for most kind of trees are still unknown.  Although for several classes of trees such as paths, stars, caterpillars, homogeneous firecrackers and others, we do know their partition dimensions.  In this paper, we determine the partition dimension of a subdivision of a particular tree, namely homogeneous firecrackers. Let G be any graph. For any positive integer k and e \in E(G), a subdivision of a graph G, denoted by S(G(e;k)), is the graph obtained from G by replacing an edge $e$ with a (k+1)-path. We show that the partition dimension of S(G(e;k)) is equal to the partition dimension of G if G is a homogeneous firecracker. We show that the partition dimension of S(G(e;k)) is equal to the partition dimension of G if G is a homogeneous firecracker. 
The signed Roman domatic number of a digraph Seyed Mahmoud Sheikholeslami; Lutz Volkmann
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 1 (2015): 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.2015.3.1.9

Abstract

Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function  $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v]$ consists of $v$ andall inner neighbors of $v$, and every vertex $u\in V(D)$ for which $f(u)=-1$ has an innerneighbor $v$ for which $f(v)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct signedRoman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le 1$ for each$v\in V(D)$, is called a {\em signed Roman dominating family} (of functions) on $D$. The maximumnumber of functions in a signed Roman dominating family on $D$ is the {\em signed Roman domaticnumber} of $D$, denoted by $d_{sR}(D)$. In this paper we initiate the study of signed Romandomatic number in digraphs and we present some sharp bounds for $d_{sR}(D)$. In addition, wedetermine the signed Roman domatic number of some digraphs.  Some of our results are extensionsof well-known properties of the signed Roman domatic number of graphs.
Some families of graphs with no nonzero real domination roots Somayeh Jahari; Saeid Alikhani
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): 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.2018.6.1.2

Abstract

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G, x) = ∑ni = γ(G)d(G, i)xi, where d(G, i) is the number of dominating sets of G of size i and γ(G) is the domination number of G. A root of D(G, x) is called a domination root of G. Obviously, 0 is a domination root of every graph G with multiplicity γ(G). In the study of the domination roots of graphs, this naturally raises the question: Which graphs have no nonzero real domination roots? In this paper we present some families of graphs whose have this property.
The consecutively super edge-magic deficiency of graphs and related concepts Rikio Ichishima; Francesc A Muntaner-Batle; Akito Oshima
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.2020.8.1.6

Abstract

A bipartite graph G with partite sets X and Y is called consecutively super edge-magic if there exists a bijective function f : V(G) ⋃ E(G) → {1,2,...,|V(G)| + |E(G)|} with the property that f(X) = {1,2,...,|X|}, f(Y) = {|X|+1, |X|+2,...,|V(G)|} and f(u)+f(v) +f(uv) is constant for each uv ∈ E(G). The question studied in this paper is for which bipartite graphs it is possible to add a finite number of isolated vertices so that the resulting graph is consecutively super edge-magic. If it is possible for a bipartite graph G, then we say that the minimum such number of isolated vertices is the consecutively super edge-magic deficiency of G; otherwise, we define it to be +∞. This paper also includes a detailed discussion of other concepts that are closely related to the consecutively super edge-magic deficiency.
Enforced hamiltonian cycles in generalized dodecahedra Maria Timkova
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.2013.1.2.1

Abstract

The H-force number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with |W| = k such that each cycle passing through all vertices of W is a hamiltonian cycle. In this paper, we determine the H-force numbers of generalized dodecahedra.

Page 6 of 39 | Total Record : 382

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