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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 15 Documents
 1   2 
Search results for , issue "Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications" : 15 Documents clear
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.
The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths Bety Hayat Susanti; A.N.M. Salman; Rinovia Simanjuntak
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.2020.8.1.11

Abstract

An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there exists a rainbow k-connected coloring for G. In this paper, we are able to find sharp lower and upper bounds for the rainbow 2-connection number of Cartesian products of arbitrary 2-connected graphs and paths. We also determine the rainbow 2-connection number of the Cartesian products of some graphs, i.e. complete graphs, fans, wheels, and cycles, with paths.
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.
On central-peripheral appendage numbers of uniform central graphs Sul-Young Choi; Jonathan Needleman
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.2020.8.1.12

Abstract

In a uniform central graph (UCG) the set of eccentric vertices of a central vertex is the same for all central vertices. This collection of eccentric vertices is the centered periphery. For a pair of graphs (C,P) the central-peripheral appendage number, Aucg(C,P), is the minimum number vertices needed to be adjoined to the graphs C and P in order to construct a uniform central graph H with center V(C) and centered-periphery V(P). We compute Aucg(C,P) in terms of the radius and diameter of P and whether or not C is a complete graph. In the process we show Aucg(C, P) ≤ 6 if diam(P) > 2.   We also provide structure theorems for UCGs in terms of the centered periphery.
Independent strong domination in complementary prisms Zeynep Nihan Berberler; Murat Ersen Berberler
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.2020.8.1.1

Abstract

Let G = (V, E) be a graph and u,v ∈ V. Then, u strongly dominates  v if (i) uv ∈ E  and (ii) deg(u) ≥ deg(v). A set D ⊂ V  is a strong-dominating set of  G  if every vertex in V-D is strongly dominated by at least one vertex in D. A set D ⊆ V  is an independent set if no two vertices of D  are adjacent. The independent strong domination number is(G) of a graph G is the minimum cardinality of a strong dominating set which is independent. Let Ġ   be the complement of a graph G. The complementary prism GĠ  of G  is the graph formed from the disjoint union of G  and  Ġ by adding the edges of a perfect matching between the corresponding vertices of G and Ġ. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.
The rainbow k-connectivity of the non-commutative graph of a finite group Luis A. Dupont; Raquiel López; Miriam Rodríguez
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.2020.8.1.7

Abstract

The non-commuting graph Γ(G) of a non-abelian group G is defined as follows. The vertex set V(Γ(G)) of ℾ(G) is G \ Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ≠ yx. We prove that the rainbow k-connectivity of Γ(G) is equal to ⌈k/2⌉ + 2, for 3 ≤ k ≤ |Z(G)|.
On cycle-irregularity strength of ladders and fan graphs Faraha Ashraf; Martin Baca; Andrea Semanicova-Fenovcikova; Suhadi Wido Saputro
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.2020.8.1.13

Abstract

A simple graph G = (V(G),E(G)) admits an H-covering if every edge in E(G) belongs to at least one subgraph of G isomorphic to a given graph H. A total k-labeling φ : V(G) ∪ E(G) → {1,2,..., k} is called to be an H-irregular total k-labeling of the graph G admitting an H-covering if for every two different subgraphs H' and H" isomorphic to H there is wtφ(H') ≠ wtφ(H"), where wtφ(H)= ∑v ∈ V(H) φ(v) + ∑e ∈ E(H) φ(e). The total H-irregularity strength of a graph G, denoted by ths(G,H), is the smallest integer k such that G has an H-irregular total k-labeling. In this paper we determine the exact value of the cycle-irregularity strength of ladders and fan 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.  
Determining the robustness of an interdependent network with a hypergraph model Gholam Hasan Shirdel; Ameneh Mortezaee
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.2020.8.1.8

Abstract

The world is included of various entities and complex interdependencies between them that can be appeared in multi-layered networks. It may be the acting of some of these entities depends on the acting of the others such that the failure in one entity may cause failures in a number of others. In this paper we try to model these complex interdependencies in a interdependent network with a directed hypergraph model and then we propose an algorithm to determine minimum number of failure for total failure in the power grid and communication network as a special interdependent network. 
Three-colour bipartite Ramsey number R_b(G_1,G_2,P_3) R Lakshmi; D.G. Sindhu
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.2020.8.1.14

Abstract

For simple bipartite graphs G1, G2, G3, the three-colour bipartite graph Ramsey number Rb(G1,G2,G3) is defined as the least positive integer n such that any 3-edge-colouring of Kn,n assures a monochromatic copy of Gi in the ith colour for some i, i ∈ {1,2,3}. In this paper, we consider the three-colour bipartite Ramsey number Rb(G1,G2,P3). Exact values are determined when G1 = G2 = C4 and when (G1,G2) = (a bistar, a bistar). For integers m,n ≥ 2, a recursive upper bound, Rb(Km,m,Kn,n,P3) ≤ Rb(Km-1,m-1,Kn,n,P3) + Rb(Km,m,Kn-1,n-1,P3) + 3,  is given. When G1 and G2 are even cycles, a lower bound is provided. In addition to these results, we have obtained the relations: R(G,K1,n) ≤ Rb(G,K1,n+1) and R(G,H) ≤ Rb(G,H,P3).

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