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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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A note on edge-disjoint contractible Hamiltonian cycles in polyhedral maps Ashish K Upadhyay; Dipendu Maity
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 2 (2014): 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.2014.2.2.8

Abstract

We present a necessary and sufficient condition for existence of edge-disjoint contractible Hamiltonian Cycles in the edge graph of polyhedral maps.
The competition numbers of Johnson graphs with diameter four Kijung Kim
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.2017.5.2.7

Abstract

In 2010, Kim, Park and Sano studied the competition numbers of Johnson graphs. They gave the competition numbers of J(n,2) and J(n,3).In this note, we consider the competition number of J(n,4).
Counting and labeling grid related graphs Christian Barrientos; Sarah Minion
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.2019.7.2.11

Abstract

In this work we explore some graphs associated with the grid Pm × Pn. A fence is any subgraph of the grid obtained by deleting any feasible number of edges from some or all the copies of Pm. We present here a closed formula for the number of non-isomorphic fences obtained from Pm × Pn, for every m, n ≥ 2. A rigid grid is a supergraph of the grid, where for every square a pair of opposite vertices are connected; we show that the number of fences built on Pm × Pn is the same that the number of rigid grids built on Pm × Pn + 1. We also introduce a substitution scheme that allows us to substitute any interior edge of any Pm in an α-labeled copy of Pm × Pn to obtain a new graph with an α-labeling. This process can be iterated multiple times on the n copies of Pm; in this way we prove the existence of an α-labeling for any graph obtained via these substitutions; these graphs form a quite robust family of α-graphs where the grid is one of its members. We also show two subfamilies of disconnected graphs that can be obtained using this scheme, proving in that way that they are also α-graphs.
On the domination and signed domination numbers of zero-divisor graph Ebrahim Vatandoost; Fatemeh Ramezani
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.2016.4.2.3

Abstract

Let $R$ be a commutative ring (with 1) and let $Z(R)$ be its set of zero-divisors. The zero-divisor graph $\Gamma(R)$ has vertex set $Z^*(R)=Z(R) \setminus \lbrace0 \rbrace$ and for distinct $x,y \in Z^*(R)$, the vertices $x$ and $y$ are adjacent if and only if $xy=0$. In this paper, we consider the domination number and signed domination number on zero-divisor graph $\Gamma(R)$ of commutative ring $R$ such that for every $0 \neq x \in Z^*(R)$, $x^2 \neq 0$. We characterize $\Gamma(R)$ whose $\gamma(\Gamma(R))+\gamma(\overline{\Gamma(R)}) \in \lbrace n+1,n,n-1 \rbrace$, where $|Z^*(R)|=n$.
A note on Fibonacci and Lucas number of domination in path Leomarich F Casinillo
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.2018.6.2.11

Abstract

Let G = (V(G), E(G)) be a path of order n ≥ 1. Let fm(G) be a path with m ≥ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set F(G) contains all possible fm(G), m ≥ 0, having the cardinality of the Fibonacci number Fn + 2. Let Fd(G) be a set of fm(G) where m = i(G) and Fdmax(G) be a set of paths with maximum independent dominating vertices. Let lm(G) be a path with m ≥ 0 independent dominating vertices which follows a Lucas string of binary numbers where 1 is the dominating vertex. A set L(G) contains all possible lm(G), m ≥ 0, having the cardinality of the Lucas number Ln. Let Ld(G) be a set of lm(G) where m = i(G) and Ldmax(G) be a set of paths with maximum independent dominating vertices. This paper determines the number of possible elements in the sets Fd(G), Ld(G), Fdmax(G) and Ldmax(G) by constructing a combinatorial formula. Furthermore, we examine some properties of F(G) and L(G) and give some important results.
Total Roman domination for proper interval graphs Abolfazl Poureidi
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.2020.8.2.16

Abstract

A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v) with f(u) > 0. The weight of a total Roman dominating function f on G is equal to f(V)=Σv ∈ Vf(v). The minimum weight of a total Roman dominating function on G is called the total Roman domination number of G. In this paper, we give an algorithm to compute the total Roman domination number of a given proper interval graph G=(V,E) in O(|V|) time.
Ideal basis in constructions defined by directed graphs Jemal Abawajy; Andrei Kelarev; Joe Ryan
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.2015.3.1.5

Abstract

The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication systems. Our main theorem establishes that, for every balanced digraph and each idempotent semiring with identity element, the incidence semiring of the digraph has a convenient visible ideal basis. It also shows that the elements of the basis can always be used to generate ideals with the largest possible weight among the weights of all ideals in the incidence semiring.
On H-irregularity strengths of G-amalgamation of graphs Faraha Ashraf; Martin Baca; Andrea Semanicova-Fenovcikova; Ayesha Shabbir
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.2017.5.2.13

Abstract

A simple graph G=(V(G),E(G)) admits an H-covering if every edge in E(G) belongs at least to one subgraph of G isomorphic to a given graph H. Then the graph G admitting H-covering admits an H-irregular total k-labeling f: V(G) U E(G) \to {1, 2, ..., k} if for every two different subgraphs H' and H'' isomorphic to H there is $wt_{f}(H') \neq wt_{f}(H'')$, where $wt_{f}(H)= \sum \limits_{v\in V(H)} f(v) + \sum \limits_{e \in E(H)} f(e)$ is the associated H-weight. The minimum k for which the graph G has an H-irregular total k-labeling is called the total H-irregularity strength of the graph G.In this paper, we obtain the precise value of the total H-irregularity strength of G-amalgamation of graphs.
C_4 decomposition of the tensor product of complete graphs Opeyemi Oyewumi; Abolape Deborah Akwu
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.2020.8.1.2

Abstract

Let G be a simple and finite graph. A graph is said to be decomposed into subgraphs H1 and H2 which is denoted by G = H1 ⊕ H2, if G is the edge disjoint union of H1 and H2. If G = H1 ⊕ H2 ⊕ H3 ⊕ ... ⊕ Hk, where H1, H2, H3, ..., Hk are all isomorphic to H, then G is said to be H-decomposable. Futhermore, if H is a cycle of length m then we say that G is Cm-decomposable and this can be written as Cm|G. Where G × H denotes the tensor product of graphs G and H, in this paper, we prove the necessary and sufficient conditions for the existence of C4-decomposition of Km × Kn. Using these conditions it can be shown that every even regular complete multipartite graph G is  C4-decomposable if the number of edges of G is divisible by 4.  
The method of double chains for largest families with excluded subposets Peter Burcsi; Daniel T. Nagy
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.2013.1.1.4

Abstract

For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $\mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many  $P$ posets. These posets are built from seven base posets using two operations. For arbitrary posets, an upper bound is given for $La(n,P)$ depending on $|P|$ and the size of the longest chain in $P$. To prove these theorems we introduce a new method, counting the intersections of $\mathcal{F}$ with double chains, rather than chains.

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