On The Existence of Non-Diregular Digraphs of Order Two Less than the Moore Bound

A communication network can be modelled as a graph or a directed graph, where each processing element is represented by a vertex and the connection between two processing elements is represented by an edge (or, in case of directed connections, by an arc). When designing a communication network, there are several criteria to be considered. For example, we can require an overall balance of the system. Given that all the processing elements have the same status, the flow of information and exchange of data between processing elements will be on average faster if there is a similar number of interconnections coming in and going out of each processing element, that is, if there is a balance (or regularity) in the network. This means that the in-degree and out-degree of each vertex in a directed graph (digraph) must be regular. In this paper, we present the existence of digraphs which are not diregular (regular out-degree, but not regular in-degree) with the number of vertices two less than the unobtainable upper bound for most values of out-degree and diameter, the so-called Moore bound

SUPER (a,d)-EDGE ANTIMAGIC TOTAL LABELING OF PENTAGONAL CHAIN GRAPH

Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f: V(G)E(G) {1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge-antimagic total properties of connected PCn by using deductive axiomatic and the pattern recognition method. The result shows that a connected pentagonal chain graphs admit a super (a,d)-edge antimagic total  labeling for d = 0,1,2 for n It can be concluded that the result of this research has covered all the feasible d. Key Words: (a,d)-edge antimagic vertex labeling, super (a,d)-edge antimagic total labeling, Pentagonal Chain Graph

On Total Vertex Irregularity Strength of Cocktail Party Graph

A vertex irregular total k-labeling of a graph G is a function λ from both the vertex and the edge sets to {1,2,3,,k} such that for every pair of distinct vertices u and x, λ(u)+∑λ(uv)≠λ(x)+∑λ(xy). uv∈E xy∈E. The integer k is called the total vertex irregularity strength, denoted by tvs (G ) , is the minimum value of the largest label over all such irregular assignments. In this paper, we prove that the total vertex irregularity strength of the Cocktail Party graph H2,n ,that is tvs(H2,n )= 3 for n ≥ 3

SUPER (a,d)-EDGE ANTIMAGIC TOTAL LABELING OF CONNECTED TRIBUN GRAPH

Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f:V(G)∪E(G)⟶{1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv∈E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge-antimagic total properties of connected Tribun graph. The result shows that a connected Tribun graph admit a super(a,d)-edge antimagic total labeling ford=0,1,2 for n≥1. It can be concluded that the result of this research has covered all the feasible n,d. Key Words: (a,d)-edge antimagic vertex labeling, super(a,d)-edge antimagic total labeling, Tribun Graph.

SUPER (a,d)-EDGE ANTIMAGIC TOTAL LABELING OF CONNECTED LAMPION GRAPH

Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f: V(G)E(G) {1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a,d)-edge-antimagic total properties of connected £n,m by using deductive axiomatic and the pattern recognition method. The result shows that a connected Lampion graphs admit a super (a,d)-edge antimagic total  labeling for d = 0,1,2 for n It can be concluded that the result of this research has covered all the feasible d. Key Words: (a,d)-edge antimagic vertex labeling, super (a,d)-edge antimagic total labeling, Lampion Graph.

SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH

Abstract. An  (a, d)-edge-antimagic  total   labeling  of G  is a  one-to-one  mapping taking the vertices and edges onto {1, 2, 3, . . . , p + q} Such that the edge-weights w(uv)  = (u)+(v)+(uv), uv ∈ E(G)  form an arithmetic sequence {a, a+d, a+2d, . . . , a+ (q − 1)d}, where first term  a > 0 and  common  difference d ≥ 0.  Such a graph G is called super if the smallest possible labels appear on the vertices.  In this paper we will study a super edge-antimagic total labelings properties of connective Swn graph.   The result shows that a connected Silkworm graph admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all the feasible n, d.   Key Words: (a, d)-edge-antimagic total labeling, super (a, d)-edge-antimagic total labeling, Silkworm graph

NILAI KETAKTERATURAN TOTAL SISI DARI GRAF GUNUNG BERAPI

Abstract. For a simple undirected connected graph G(V,E) with vertex set V and edge set E a labeling : V E → {1, 2, 3, ..., k} is called a total k-labeling. A total k-labeling is defined to be an edge irregular total k-labeling of the graph G if for every two different edges uv and xy of G there is t(uv) ≠ t(xy). The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of the graph G, denoted by tes(G). In this paper, we determine the total edge irregularity strength of volcano graph tes(Gbm,n) and the total edge irregularity strength of s copies volcano graph tes(sGbm,n). Key Words : edge irregular total labeling, total edge irregularity strength, volcano grap

Penerapan Pembelajaran Kooperatif Teknik Kancing Gemerincing berbantuan Facebook Untuk Meningkatkan Aktivitas dan Hasil Belajar Siswa Sub Pokok Bahasan Persegi Panjang dan Persegi kelas VIIE SMP Negeri 2 Tanggul Tahun Ajaran 2013/2014

Abstrak. Penelitian ini diselenggarakan dalam 2 siklus agar dapat menambah aktivitas dan hasil belajar siswa. Penelitian ini menggunakan model pembelajaran kooperatif teknik kancing gemerincing berbantuan facebook untuk memberikan kesempatan kepada siswa dalam memberikan kontribusi serta pandangan dan pemikiran dalam berkelompok. Penelitian yang digunakan adalah Class Action Research (CAR) dengan pendekatan yang berkualitas dan berkuantitas. Metode pengumpulan data yang digunakan adalah observasi, dokumentasi, tes dan wawancara.Hasil penelitian yang dapat menambah aktivitas siswa, hasil pembelajaran yang lengkap dan daya tarik siswa. Dapat disimpulkan bahwa adanya peningkatan kegiatan dan hasil belajar siswa. Kata Kunci : teknik kancing gemerincing, facebook, hasil pembelajaran

Finite Difference Method and Newton's Theorem to Determine the Sum of Series

Problems that are often faced to prove the truth of a formula if the presented series is a series that is not the formula of arithmetic and geometric series. One proof among the most commonly proofs used is the proof by mathematical induction. This study was conducted to determine the sum of the first n terms formula of: (1) arithmetic series, storied arithmetic series with the basis of arithmetic series, (2) geometric series, (3) storied arithmetic series with the basis of geometric series, and (4) series which are not arithmetic and geometric series that the formula of the n terms is given, by using the finite difference method and Newton's theorem. The formula of the sum of the first n terms obtained from the results of this study and then it is verified by using mathematical induction. Keywords : Series, finite difference, mathematical induction, Newton’s theore

PENGEMBANGAN PERANGKAT PEMBELAJARAN BERBASIS METODE GUIDED DISCOVERY LEARNING BERBANTUAN E-LEARNING DENGAN APLIKASI ATUTOR PADA POKOK BAHASAN LINGKARAN KELAS VIII SMP

Abstract.The research aims to know process and result of developing of mathematics learning intruments based on guided discovery learning method and assisted e-learning with Learning Management System (LMS)ATutor for circle topic at seventh grade of junior high school. The research development modle refers to 4D Thiagarajan models. The subject of research is students of VIIIG class SMPN 7Jember in even semester academic year 2012-2013. The data of research are obtained by validation sheet, observation sheet of teacher and students activities, questionnaire, and evaluation test.The products of this research are lesson plan, studenthandbook, digital worksheet, and evaluation test integrated by e-learning site.The result shows that the learning instruments satisfy validity, practical, and effective criteria. Key Words: guided discovery learning, e-learning, LMS ATutor, circl