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CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Published by Universitas Jember
ISSN : -     EISSN : 27227774     DOI : https://doi.org/10.25037/cgantjma
Core Subject : Science, Education,
Computer Science & IT Other
Subjects suitable for publication include, the following fields of: Degree Diameter Problem in Graph Theory Large Graphs in Computer Science Mathematical Computation of Graph Theory Graph Coloring in Atomic and Molecular Graph Labeling in Coding Theory and Cryptography Dimensions of graphs on Control System Rainbow Connection in Delivery Design System Ramsey Theory and Its Application on Physics Graph Theory in Communication and Electrical Networks Graph Theory in Quantum Mechanics and Thermodynamics Spectral Graph Theory in Vibration and Noise Graph Theory in Statistical Physics and Mechanics Graph theory in Network of Quantum Oscillators Applied Mathematics on Environment, Biophysics and Engineering Machine Learning and Artificial Neural Networks Mathematical and Computational Education
Arjuna Subject : Matematika - Matematika Diskrit dan Kombinatori
Articles 9 Documents
 1 
Search results for , issue "Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS" : 9 Documents clear
On the Domination Number of Some Graph Operations N Y. Sari; I H. Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (823.596 KB) | DOI: 10.25037/cgantjma.v1i1.4

Abstract

A set D of vertices of a simple graph G, that is a graph without loops and multiple edges, is called a dominating set if every vertex u ∈ V (G) − D is adja-cent to some vertex v ∈ D. The domination number of a graph G, denoted by γ(G), is the order of a smallest dominating set of G. A dominating set D with |D| = γ(G) is called a minimum dominating set. This research aims to char-acterize the domination number of some graph operations, namely joint graphs, coronation of graphs, graph compositions, tensor product of two graphs, and graph amalgamation. The results shows that most of the resulting domination numbers attain the given lower bound of γ(G). Keywords: Dominating set, domination number,
Chromatics Number of Operation Graphs Kiki Kurdianto; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1540.524 KB) | DOI: 10.25037/cgantjma.v1i1.9

Abstract

Let G = (V (G); E(G)) be connected nontrivial graph. Edge coloring is de-¯ned as c : E(G) ! f1; 2; :::; kg; k 2 N, with the conditions no edges adja-cent having the same color. Coloring k-color edges r-dynamic is edges color-ing as much as k color such that every edges in E(G) with adjacent at least minfr; d(u) + d(v) ¡ 2g have di®erent color. An Edge r dynamic is a proper c of E(G) such that jc(N(uv))j = minfr; d(u) + d(v) ¡ 2g, for each edge N(uv) is the neighborhood of uv and c(N(uv)) is color used to with adjacent edges of uv. the edge r-dynamic chromatic number, written as ¸(G), is the minimum k such that G has an edge r-dynamic k-coloring. chromatic number 1-dynamic writ-ten as ¸(G), chromatic number 2-dynamic written as ¸d(G) And for chromatic number r-dynamic written as ¸(G). A graph is used in this research namely gshack(H3; e; n), amal(Bt3; v; n) and amal(S4; v; n). Keywords: r-dynamic coloring, r-dynamic chromatic number, graph operations.
Super (a; d) - Face Antimagic Total Labeling of Connective Shackle Graph (C5; e; n) Siska Binastuti; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2425.018 KB) | DOI: 10.25037/cgantjma.v1i1.5

Abstract

Let G be a simple graph of order p, size q and face r. The graph G is called a super (a; d) - face antimagic total labeling , if there exist a bijection f : V (G) [ E(G) [ F (G) ! f1; 2; :::; p + q + rg such that the set of s-sided face weights, Ws = fas; as + d; as + 2d; :::; as + (rs ¡1)dg form an arithmetic sequence with ¯rst term a,common di®erence d, where a and d are positive integers s and rs is the number of s-sided faces. Such a graph is called super if the smallest possible labels appear on the vertices. The type of Face Antimagic Labeling is (1,1,1). In this paper, describe of Super (a; d) - Face Antimagic of Connective Shackle (C5; e; n) Graph. Keywords: Super (a; d)-face antimagic total labeling, face antimagic la-beling.
Dominating Set of Operation of Special Graphs Hendry Dwi Saputro; Ika Hesti A.; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1663.028 KB) | DOI: 10.25037/cgantjma.v1i1.11

Abstract

A set D of vertices of a simple graph G, that is a graph without loops and multiple edges, is called a dominating set if every vertex u 2 V (G) D is adja-cent to some vertex v 2 D. The domination number of a graph G, denoted by (G), is the order of a smallest dominating set of G. A dominating set D with jDj = (G) is called a minimum dominating set. We will show dominating set of graph operation of special graph (Pn, Km, cycle Cn, Wm, ladder Ln, Btm, and special graph G1, G2.
Independent Domination Number of Operation Graph Siti Aminatus Solehah; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (976.66 KB) | DOI: 10.25037/cgantjma.v1i1.6

Abstract

Let G be a simple, undirected and connected graph. An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u ∈ V (G) − D is adjacent to some vertex v ∈ D. A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. A minimum independent dominating set is an independent set of smallest possible size for a given graph G. This size is called the independence number of G, and denoted i(G). Operation Graph is a technical to get a new graph types by performing the operation of two or more graphs. Power Graph is a operation graph where let the graph G and H , notation of the power graph is (GH ). Keywords: r-dynamic coloring, r-dynamic chromatic number, graph operations. 
On r-Dynamic Coloring for Graph Operation of Cycle, Star, Complete, and Path Desy Tri Puspasari; Dafik Dafik; Slamin Slamin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2952.959 KB) | DOI: 10.25037/cgantjma.v1i1.2

Abstract

For integer k, r > 0, (k, r) -coloring of graph G is a proper coloring on the vertices of G by k-colors such that every vertex v of degree d(v) is adjacent to vertices with at least min{d(v), r} different color. By a proper k -coloring of graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices are different color. An r -dynamic k -coloring is a proper k -coloring c of G such that |c(N (v))| ≥ min{r, d(v)} for each vertex v in V (G), where N (v) is the neighborhood of v and c(S) = {c(v) : v ∈ S} for a vertex subset S . The r-dynamic chromatic number, written as χr (G), is the minimum k such that G has an r-dynamic k-coloring. Note the 1-dynamic chromatic number of graph is equal to its chromatic number, denoted by χ(G), and the 2-dynamic chromatic number of graph denoted by χd (G). By simple observation with a greedy coloring algorithm, it is easy to see that χr (G) ≤ χr+1(G), however χr+1(G) − χr (G) does not always have the same difference. Thus finding an exact values of χr (G) is significantly useful. In this paper, we investigate the some exact value of χr (G) when G is for an operation product of cycle, star, complete, and path graphs.
Analysis Super (a; d)-S3 Antimagic Total Dekomposition of Helm Graph Connektive for Developing Ciphertext Kholifatur Rosyidah; Dafik Dafik; Susi Setiawani
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1521.163 KB) | DOI: 10.25037/cgantjma.v1i1.7

Abstract

Covering of G is H = fH1; H2; H3; :::; Hkg subgraph family from G with every edges on G admit on at least one graph Hi for a i 2 f1; 2; :::; kg. If every i 2 f1; 2; :::; k g, Hi isomorphic with a subgraph H, then H said cover-H of G. Furthermore, if cover-H of G have a properties is every edges G contained on exactly one graph Hi for a i 2 f1; 2; :::; kg, then cover-H is called decomposition-H. In this case, G is said to contain decomposition-H. A graph G(V; E) is called (a; d)-H total decomposition if every edges E is sub graph of G isomorphic of H. In this research will be analysis of super (a; d)-S3 total decomposition of connective helm graph to developing ciphertext.Key Word : Super (a; d)-S3, Dekomposisi, Graf helm, dan Ciphertext 
Super (a; d)-edge Antimagic Total Labeling of Shack(F6; B2; n) Graph for Developing a Polyalphabetic Cryptosystem Arnasyitha Yulianti Soelistya; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1651.662 KB) | DOI: 10.25037/cgantjma.v1i1.3

Abstract

A graph G of order p and size q is called an (a; d)-edge-antimagic total if there exist a bijection f : V (G) [ E(G) ! f1; 2; : : : ; p + qg such that the edge-weights, w(uv) = f(u) + f(v) + f(uv); uv 2 E(G), form an arithmetic sequence with ¯rst term a and common di®erence d. Such a graph is called super if the smallest possible labels appear on the vertices. In this paper we study a super edge-antimagic total labeling of Shackle (F6; B2; n) Graph connected and we will use it to develop a polyalphabetic cryptosystem.
Super (a; d)-H-Antimagic Total Covering of Triangular Cycle Ladder Graph for Developing Ciphertext Irma Azizah; Dafik Dafik; Slamin Slamin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2818.788 KB) | DOI: 10.25037/cgantjma.v1i1.8

Abstract

A (a; d)-H-antimagic total covering is a total labeling dari V (G) [ E(G) to integer number f1; 2; 3; :::; jV (G) [ E(G)jg with condition, every subgraph A inP P PG isomorphic with subgraph H A = v2V (A) (v) + e2E(A) (e) on arith-metic sequence. A graph containing the labeling called super (a; d)-H-antimagic total covering. Furthermore , f (v)gv2V = f1; :::; jV jg, is called graph super H antimagic. In this research used triangular Cycle Ladder Graph T CLn of con-nective to developing ciphertext. Key Word : Super H antimagic total selimut, Triangular Cycle Ladder Graph T CLn, Ciphertexts.

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