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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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Degree equitable restrained double domination in graphs Sunilkumar M Hosamani; Shailaja Shirkol; Preeti B. Jinagouda; Marcin Krzywkowski
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.2021.9.1.10

Abstract

A subset D ⊆ V(G) is called an equitable dominating set of a graph G if every vertex v ∈ V(G) \ D has a neighbor u ∈ D such that |dG(u)-dG(v)| ≤ 1. An equitable dominating set D is a degree equitable restrained double dominating set (DERD-dominating set) of G if every vertex of G is dominated by at least two vertices of D, and 〈V(G) \ D〉 has no isolated vertices. The DERD-domination number of G, denoted by γcl^e(G), is the minimum cardinality of a DERD-dominating set of G. We initiate the study of DERD-domination in graphs and we obtain some sharp bounds. Finally, we show that the decision problem for determining γcl^e(G) is NP-complete.
Hyper-Hamiltonian circulants Zbigniew R. Bogdanowicz
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.2021.9.1.16

Abstract

A Hamiltonian graph G = (V,E) is called hyper-Hamiltonian if G-v is Hamiltonian for any v ∈ V(G). G is called a circulant if its automorphism group contains a |V(G)|-cycle.  First, we give the necessary and sufficient conditions for any undirected connected circulant to be hyper-Hamiltonian. Second, we give necessary and sufficient conditions for a connected circulant digraph with two jumps to be hyper-Hamiltonian. In addition, we specify some sufficient conditions for a circulant digraph with arbitrary number of jumps to be hyper-Hamiltonian.
Some new results on the b-domatic number of graphs Mohamed Benattalah; Mustapha Chellali; Noureddine Ikhlef-Eschouf
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.2021.9.1.5

Abstract

A domatic partition P of a graph G=(V,E) is a partition of V into classes that are pairwise disjoint dominating sets. Such a partition P is called b-maximal if no larger domatic partition P' can be obtained by gathering subsets of some classes of P to form a new class. The b-domatic number bd(G) is the minimum cardinality of a b-maximal domatic partition of G. In this paper, we characterize the graphs G of order n with bd(G) ∈ {n-1,n-2,n-3}. Then we prove that for any graph G on n vertices, bd(G)+bd(Ġ) ≤ n+1, where Ġ is the complement of G. Moreover, we provide a characterization of the graphs G of order n with bd(G)+bd(Ġ) ∈ {n+1,n} as well as those graphs for which bd(G)=bd(Ġ)=n/2.
Connected domination value in graphs Angsuman Das
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.2021.9.1.11

Abstract

In a connected graph G = (V,E), a set D ⊂ V is a connected dominating set if for every vertex v ∈ V \ D, there exists u ∈ D such that u and v are adjacent, and the subgraph〈D〉induced by D in G is connected. A connected dominating set of minimum cardinality is called a γc-set of G. For each vertex v ∈ V, we define the connected domination value of v to be the number of γc-sets of G to which v belongs. In this paper, we study the properties of connected domination value of a connected graph G and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of γc-sets for a few well-known family of graphs.
A note on nearly Platonic graphs with connectivity one Dalibor Froncek; Mahdi Reza Khorsandi; Seyed Reza Musawi; Jiangyi Qiu
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.2021.9.1.17

Abstract

A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with connectivity one can exist. This complements a recent result by Keith, Froncek, and Kreher on non-existence of 2-connected nearly Platonic graphs.
Automorphism groups of some families of bipartite graphs K.G. Sreekumar; K. Manilal
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.2021.9.1.6

Abstract

This paper discusses the automorphism group of a  class of  weakly semiregular bipartite graphs and its subclass called WSBEND graphs.  It also tries to analyse the  automorphism group of the SM sum graphs and SM balancing graphs.  These graphs  are weakly semiregular bipartite graphs too.  The SM sum graphs  are particular cases  of bipartite Kneser graphs. The  bipartite Kneser type graphs are defined on n-sets for a fixed positive integer n. The  automorphism groups of the bipartite Kneser type graphs are related to that of weakly semiregular bipartite graphs.  Weakly semiregular bipartite  graphs  in which   the neighbourhoods of the vertices in the SD part having  the same degree sequence, possess  non trivial automorphisms.  The automorphism groups of SM sum graphs are isomorphic to the  symmetric groups. The relationship between the  automorphism groups of SM balancing  graphs  and  symmetric  groups are established here.   It has been observed by using the well known algorithm Nauty, that the size of automorphism  groups of SM balancing graphs are prodigious.  Every weakly semiregular bipartite graphs with  k-NSD subparts has a matching which saturates the smaller partition. 
On two Laplacian matrices for skew gain graphs Roshni T. Roy; Shahul Hameed K.; Germina K.A.
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.2021.9.1.12

Abstract

Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. Generalizing the notion of gain graphs, skew gain graphs have the property that the gain of a reversed edge is the image of edge gain under an anti-involution. In this paper, we study two different types, Laplacian and g-Laplacian matrices for a skew gain graph where the skew gains are taken from the  multiplicative group Fx of a field F of characteristic zero. Defining incidence matrix, we also prove the matrix tree theorem for skew gain graphs in the case of the g-Laplacian matrix. 
Constructions of new integral graph families Thomas Gardemann; Katja Mönius
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.2021.9.1.18

Abstract

We construct new families of integral graphs by considering complete products, unions and point identifications of complete graphs and complete bipartite graphs. In particular, we find a relation between arithmetic series and the integrality of complete products.
Vertex partition of hypergraphs and maximum degenerate subhypergraphs Thomas Schweser; Michael Stiebitz
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.2021.9.1.1

Abstract

In 2007 Matamala proved that if G is a simple graph with maximum degree Δ ≥ 3 not containing KΔ+1 as a subgraph and s, t are positive integers such that s+t ≥ Δ, then the vertex set of G admits a partition (S,T) such that G[S] is a maximum order (s-1)-degenerate subgraph of G and G[T] is a (t-1)-degenerate subgraph of G. This result extended earlier results obtained by Borodin, by Bollobas and Manvel, by Catlin, by Gerencser and by Catlin and Lai. In this paper we prove a hypergraph version of this result and extend it to variable degeneracy and to partitions into more than two parts, thereby extending a result by Borodin, Kostochka, and Toft.
‎Distinguishing index of Kronecker product of two graphs ‎Saeid Alikhani; Samaneh Soltani
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.2021.9.1.7

Abstract

The distinguishing index D'(G)  of a graph G is the least integer d such that G has an edge labeling with d labels that is preserved only by a trivial automorphism. The Kronecker product G x H of two graphs G and H is the graph with vertex set V(G) x V(H) and edge set {{(u,x), (v,y)} |{u,v} ∈ E(G) and {x,y} ∈  E(H)}. In this paper we study the distinguishing index of Kronecker product of two graphs. 

Page 21 of 39 | Total Record : 382

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