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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 325 Documents
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Characterization of perfect matching transitive graphs Ju Zhou
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (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.2018.6.2.15

Abstract

A graph G is perfect matching transitive, shortly PM-transitive, if for any two perfect matchings M and N of G, there is an automorphism f : V(G) ↦ V(G) such that fe(M) = N, where fe(uv) = f(u)f(v). In this paper, the author proposed the definition of PM-transitive, verified PM-transitivity of some symmetric graphs, constructed several families of PM-transitive graphs which are neither vertex-transitive nor edge-transitive, and discussed PM-transitivity of generalized Petersen graphs.
Modular irregularity strength of graphs Martin Baca; Kadarkarai Muthugurupackiam; KM. Kathiresan; S. Ramya
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.2020.8.2.19

Abstract

We introduce a modular irregularity strength of graphs as modification of the well-known irregularity strength. We obtain some estimation on modular irregularity strength and determine the exact values of this parameter for five families of graphs.
A Study on Topological Integer Additive Set-Labeling of Graphs Sudev Naduvath
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.2015.3.1.8

Abstract

A set-labeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is  a set-labeling such that the induced function $f^{\oplus}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\oplus}(uv) = f(u){\oplus}f(v)$ for every $uv{\in} E(G)$ is also injective. Let $G$ be a graph and let $X$ be a non-empty set. A set-indexer $f:V(G)\to \mathcal{P}(X)$  is called a topological set-labeling of $G$ if $f(V(G))$ is a topology of $X$.  An integer additive set-labeling is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$, whose associated function $f^+:E(G)\to \mathcal{P}(\mathbb{N}_0)$ is defined by $f(uv)=f(u)+f(v), uv\in E(G)$, where $\mathbb{N}_0$ is the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ is its power set. An integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of topological set-labeling of graphs to topological integer additive set-labeling of graphs.
Upper bounds on the bondage number of a graph Vladimir Dimitrov Samodivkin
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.2018.6.1.1

Abstract

The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain sufficient conditions for the validity of the inequality b(G) ≤ 2s − 2, provided G has degree s vertices. We also present upper bounds for the bondage number of graphs in terms of the girth, domination number and Euler characteristic. As a corollary we give a stronger bound than the known constant upper bounds for the bondage number of graphs having domination number at least four. Several unanswered questions are posed.
Some new upper bounds for the inverse sum indeg index of graphs Akbar Ali; Marjan Matejic; Emina Milovanovic; Igor Milovanovic
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.2020.8.1.5

Abstract

Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex degrees (d1,d2,...,dn) where di denotes the degree of a vertex i ∈ V. With i ∼ j, we denote the adjacency of the vertices i and j in the graph G. The inverse sum indeg (ISI) index of the graph G is defined as ISI(G)=∑i∼j(didj)/(di+dj). Some new upper bounds for the ISI index are obtained in this paper.
Characterizing all trees with locating-chromatic number 3 Edy Tri Baskoro; A Asmiati
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.2013.1.2.4

Abstract

Let $c$ be a proper $k$-coloring of a connected graph $G$.  Let $\Pi = \{S_{1}, S_{2},\ldots, S_{k}\}$ be the induced  partition of $V(G)$ by $c$,  where $S_{i}$ is the partition class having all vertices with color $i$.The color code $c_{\Pi}(v)$ of vertex $v$ is the ordered$k$-tuple $(d(v,S_{1}), d(v,S_{2}),\ldots, d(v,S_{k}))$, where$d(v,S_{i})= \hbox{min}\{d(v,x)|x \in S_{i}\}$, for $1\leq i\leq k$.If all vertices of $G$ have distinct color codes, then $c$ iscalled a locating-coloring of $G$.The locating-chromatic number of $G$, denoted by $\chi_{L}(G)$, isthe smallest $k$ such that $G$ posses a locating $k$-coloring. Clearly, any graph of order $n \geq 2$ have locating-chromatic number $k$, where $2 \leq k \leq n$. Characterizing all graphswith a certain locating-chromatic number is a difficult problem. Up to now, we have known allgraphs of order $n$ with locating chromatic number $2, n-1,$ or $n$.In this paper, we characterize all trees whose locating-chromatic number $3$. We also give a family of trees with locating-chromatic number 4.
A note on the edge Roman domination in trees Nader Jafari Rad
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.2017.5.1.1

Abstract

A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the minimum cardinality taken over all edge dominating sets of $G$. An \textit{edge Roman dominating function} of a graph $G$ is a function $f : E(G)\rightarrow \{0,1,2 \}$ such that every edge$e$ with $f(e)=0$ is adjacent to some edge $e'$ with $f(e') = 2.$The weight of an edge Roman dominating function $f$ is the value$w(f)=\sum_{e\in E(G)}f(e)$. The edge Roman domination number of $G$, denoted by $\gamma_R'(G)$, is the minimum weight of an edge Roman dominating function of $G$. In this paper, we characterize trees with edge Roman domination number twice the edge domination number.
On the complexity of some hop domination parameters Nader Jafari Rad; Elahe Shabani
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.2019.7.1.6

Abstract

A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values on V. The minimum weight of an HRDF on G is called the hop Roman domination number of G. An HRDF f is a hop Roman independent dominating function (HRIDF) if for any pair v, w with f(v) > 0 and f(w) > 0, d(v, w) ≠ 2. The minimum weight of an HRIDF on G is called the hop Roman independent domination number of G. In this paper, we study the complexity of the hop independent dominating problem, the hop Roman domination function problem and the hop Roman independent domination function problem, and show that the decision problem for each of the above three problems is NP-complete even when restricted to planar bipartite graphs or planar chordal graphs.
Log-concavity of the genus polynomials of Ringel Ladders Jonathan L Gross; Toufik Mansour; Thomas W. Tucker; David G.L. Wang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (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.2015.3.2.1

Abstract

A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more graphs have log-concave genus polyno- mials. Herein we establish Ringel ladders as the first significant non-linear infinite family of graphs known to have log-concave genus polynomials. We construct an algebraic representation of self-bar-amalgamation as a matrix operation, to be applied to a vector representation of the partitioned genus distribution of a symmetric ladder. Analysis of the resulting genus polynomial involves the use of Chebyshev polynomials. This paper continues our quest to affirm the quarter-century-old conjecture that all graphs have log-concave genus polynomials.
Rainbow perfect domination in lattice graphs Luis R. Fuentes; Italo J. Dejter; Carlos A. Araujo
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.2018.6.1.7

Abstract

Let 0 < n ∈ Z. In the unit distance graph of Zn ⊂ Rn, a perfect dominating set is understood as having induced components not necessarily trivial. A modification of that is proposed: a rainbow perfect dominating set, or RPDS, imitates a perfect-distance dominating set via a truncated metric; this has a distance involving at most once each coordinate direction taken as an edge color. Then, lattice-like RPDS s are built with their induced components C having: i vertex sets V(C) whose convex hulls are n-parallelotopes (resp., both (n − 1)- and 0-cubes) and ii each V(C) contained in a corresponding rainbow sphere centered at C with radius n (resp., radii 1 and n − 2).

Page 3 of 33 | Total Record : 325

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