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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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On 2-power unicyclic cubic graphs Shariefuddin Pirzada; Mushtaq Shah; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.24

Abstract

In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are called as 2-power unicyclic cubic graphs. Further we observe that the only 2-power cycle in a cubic graph cannot be removed implying that there does not exist a counter example for Erdos-Gyárfás conjecture.
Non-inclusive and inclusive distance irregularity strength for the join product of graphs Faisal Susanto; Kristiana Wijaya; I Wayan Sudarsana; Slamin Slamin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.1

Abstract

A function ϕ: V(G)→{1, 2, …, k} of a simple graph G is said to be a non-inclusive distance vertex irregular k-labeling of G if the sums of labels of vertices in the open neighborhood of every vertex are distinct and is said to be an inclusive distance vertex irregular k-labeling of G if the sums of labels of vertices in the closed neighborhood of each vertex are different. The minimum k for which G has a non-inclusive (resp. an inclusive) distance vertex irregular k-labeling is called a non-inclusive (resp. an inclusive) distance irregularity strength and is denoted by dis(G) (resp. by dis(G)). In this paper, the non-inclusive and inclusive distance irregularity strength for the join product graphs are investigated.
Relative g-noncommuting graph of finite groups Monalisha Sharma; Rajat Kanti Nath
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.7

Abstract

Let G be a finite group. For a fixed element g in G and a given subgroup H of G, the relative g-noncommuting graph of G is a simple undirected graph whose vertex set is G and two vertices x and y are adjacent if x ∈ H or y ∈ H and [x, y]≠g, g−1. We denote this graph by ΓH, Gg. In this paper, we obtain computing formulae for degree of any vertex in ΓH, Gg and characterize whether ΓH, Gg is a tree, star graph, lollipop or a complete graph together with some properties of ΓH, Gg involving isomorphism of graphs. We also present certain relations between the number of edges in ΓH, Gg and certain generalized commuting probabilities of G which give some computing formulae for the number of edges in ΓH, Gg. Finally, we conclude this paper by deriving some bounds for the number of edges in ΓH, Gg.
Grünbaum colorings extended to non-facial 3-cycles sarah-marie belcastro; Ruth Haas
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.13

Abstract

We consider the question of when a triangulation with a Grünbaum coloring can be edge-colored with three colors such that the non-facial 3-cycles also receive all three colors; we will call this a strong Grünbaum coloring. It turns out that for the sphere, every triangulation has a strong Grünbaum coloring, and that the presence of a K5 subgraph prohibits a strong Grünbaum coloring, but that K5 is not the only such barrier. We investigate the ramifications of these facts. We also show that for every other topological surface there exist triangulations with a strong Grünbaum coloring and triangulations that have Grünbaum colorings but that cannot have a strong Grünbaum coloring. Finally, we reframe strong Grünbaum colorings as certain hypergraph edge colorings, and raise the question of how many colors are needed to achieve an edge coloring such that both facial and non-facial 3-cycles receive three colors.
Total domination number of middle graphs Farshad Kazemnejad; Behnaz Pahlavsay; Elisa Palezzato; Michele Torielli
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.19

Abstract

A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set. In this paper, we study the total domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph. We also compute the total domination number of the middle graph of some known families of graphs explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of middle graphs.
A generalization of Pappus graph Sucharita Biswas; Angsuman Das
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.25

Abstract

In this paper, we introduce a new family of cubic graphs Γ(m), called Generalized Pappus graphs, where m ≥ 3. We compute the automorphism group of Γ(m) and characterize when it is a Cayley graph.
Degree sum adjacency polynomial of standard graphs and graph operations S S Shinde; H S Ramane; S B Gudimani; N Swamy
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.2

Abstract

In this paper we explore the characteristic polynomials of degree sum adjacency matrix DSA(G) of a simple undirected graph G. We state a relation between the structure of a graph with the coefficients of its DSA polynomial. We obtain a generating function to find the number of walks of length k in a graph. Then, we obtain the degree sum adjacency polynomial for some standard graphs, derived graphs and for graph operations.
On twin edge colorings in m-ary trees Jayson De Luna Tolentino; Reginaldo M. Marcelo; Mark Anthony C. Tolentino
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.8

Abstract

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′t(G). In this paper, we study the twin edge colorings in m-ary trees for m ≥ 2; in particular, the twin chromatic indexes of full m-ary trees that are not stars, r-regular trees for even r ≥ 2, and generalized star graphs that are not paths nor stars are completely determined. Moreover, our results confirm the conjecture that χ′t(G)≤Δ(G)+2 for every connected graph G (except C5) of order at least 3, for all trees of order at least 3.
Interlace polynomials of lollipop and tadpole graphs Christina L Eubanks-Turner; Kathryn Cole; Megan Lee
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.14

Abstract

In this paper, we examine interlace polynomials of lollipop andtadpole graphs. The lollipop and tadpole graphs are similar in that they bothinclude a path attached to a graph by a single vertex. In this paper we giveboth explicit and recursive formulas for each graph, which extends the work ofArratia, Bollobas and Sorkin, among others. We also give special values,examine adjacency matrices and behavior of coecients of these polynomials.
Ramsey minimal graphs for a pair of a cycle on four vertices and an arbitrary star Maya Nabila; Hilda Assiyatun; Edy Tri Baskoro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.20

Abstract

Let F, G and H be simple graphs. The notation F → (G, H) means that for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. A graph F is called a Ramsey (G, H)-minimal graph if it satisfies two conditions: (i) F → (G, H) and (ii) F − e ↛ (G, H) for any edge e of F. In this paper, we give some finite and infinite classes of Ramsey (C4, K1, n)-minimal graphs for any n ≥ 3.

Page 26 of 39 | Total Record : 382

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