We consider that all graph in this paper are finite, simple and connected graph. A graceful k−coloring of a graph is a proper vertex coloring f : V(G) → {1, 2, ..., k}, where k ≥ 2 which induces a ...proper edge coloring f' : E(G) → {1, 2, ..., k − 1} defined by f' (uv) = |f(u) − f(v)|. A vertex coloring f of graph is a graceful coloring if f is a graceful k−coloring for k ≥ 2. The minimum k for which a graph G has a graceful k−coloring is called a graceful chromatic number of a graph G, denoted by χg(G). In our paper, we will investigate the establish exact value of graceful chromatic number of unicyclic graph namely (m, n)−tadpole graph, n−pan graph and sun graphs
Abstract
Technological developments are currently entering the industrial revolution 4.0 where everything is digital based. Learning media are tools used by educators in carrying out learning ...activities. One of the learning media that can be applied in learning mathematics is GeoGebra software. However, the GeoGebra software does not interact between educators and students, so we need a Google Classroom to improve interactive learning that can be combined with GeoGebra Online. The process of developing interactive online learning media using Google Classroom were assisted by GeoGebra software on quadratic function material used the Thiagarajan development model which consisted of four stages, namely define, design, development and dissemination. The results of learning media validation fulfilled the validity criteria with a correlation coefficient based on the validation sheet of 0.92 which is included in the valid category with a very high interpretation. Practical criteria with a percentage of the average value of the user response questionnaire based on a user response questionnaire of 91.75% which is included in the practical category with a good percentage. The effectiveness criteria with the percentage of learning outcomes based on the learning outcomes test was 82.61% which is included in the effective category with a very good percentage. The development of instructional media tested at SMA Muhammadiyah 3 Jember has fulfilled three criteria, namely valid, practical and effective.
All graphs in this paper are simple, finite, and undirected graph. Let r be a edges of H. The edge comb product between L and H, denoted by L⊵H, is a graph obtained by taking one copy of L and |E(L)| ...copies of H and grafting the i-th copy of H at the edges r to the i-th edges of L, we call such a graph as an edge comb product of graph with subgraph as a terminal of its amalgamation, denoted by G = K⊵Amal(H, L ⊂ H, n). The graph G is said to admits an (a, d)-H-antimagic total labeling if there exist a bijection f : V(G) ∪ E(G) → {1, 2, ..., |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W (H) = ∑v∈V(H) f(v) + ∑e∈E(H) f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (t − 1)d}, where a and d are positive integers and t is the number of all subgraphs isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study the super H−antimagicness of disjoint union of edge comb product of graphs with subgraph as a terminal of its amalgamation.
The aim of this research was to compare the HIC (Highly interactive classroom) system with a traditional method of teaching superposition of wave functions courses especially. In order to examine ...it's learning effectiveness across three dimensional, knowledge, comprehension, and application. The highly interactive classroom which collaborated with proof mathematics formulation, computer programming, and cloud classroom. The study followed a pretest, posttest, and delayed posttest with the quasi-experimental design. A total of 66 students (aged 18-19 years) divided into experimental group and control group. Experimental group 33 student (10 males and 23 females) was utilizing of cloud classroom and 33 students (12 males and 21 females) in the control group. Pretest, and posttest were evaluated by using inferential statistics t-test. The significant value of t-test score is -0.817 (p < 0.05) means there are significant of post-test score between control class and experiment class. The result indicated that student on an experimental group that teaching utilizing collaboration of computer programming, and highly interactive classroom better than control group was teaching by traditional method in post-test and delayed posttest across three learning dimensions. According to these result. The collaboration of mathematics formulation, computer programming, and HIC (highly interactive cloud classroom) is recommended to be a strategy for teaching on the combination of wave function topic.
The local edge metric dimension of graph Adawiyah, R; Dafik; Alfarisi, R ...
Journal of physics. Conference series,
05/2020, Volume:
1543, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, we introduce a new notion of graph theory study, namely a local edge metric dimension. It is a natural extension of metric dimension concept. dG(e,v) = min{d(x,v),d(y,v)} is the ...distance between the vertex v and the edge xy in graph G. A non empty set S⊂V is an edge metric generator for G if for any two edges e1,e2∈E there is a vertex k∈S such that dG(k,e1≠dG(k,e2)). The minimum cardinality of edge metric generator for G is called as edge metric dimension of G, denoted by dimE(G). The local edge metric dimension of G, denoted by dimE(G), is a local edge metric generator of G if r(xk|S)≠r(yk|S) for every pair xk,ky of adjacent edges of G. Our concern in this paper is investigating some results of local edge metric dimension on some graphs.
A simple graph G=(V,E) is said to be an H-covering if every edge of G belongs to at least one subgraph isomorphic to H. A bijection f:V∪E→{1,2,3,…,V+E} is an (a,d)-H-antimagic total labeling of G if, ...for all subgraphs H′ isomorphic to H, the sum of labels of all vertices and edges in H′ form an arithmetic sequence {a,a+d,…,(k-1)d} where a>0, d≥0 are two fixed integers and k is the number of all subgraphs of G isomorphic to H. The labeling f is called super if the smallest possible labels appear on the vertices. A graph that admits (super) (a,d)-H-antimagic total labeling is called (super) (a,d)-H-antimagic. For a special d=0, the (super) (a,0)-H-antimagic total labeling is called H-(super)magic labeling. A graph that admits such a labeling is called H-(super)magic. The m-shadow of graph G, Dm(G), is a graph obtained by taking m copies of G, namely, G1,G2,…,Gm, and then joining every vertex u in Gi, i∈{1,2,…,m-1}, to the neighbors of the corresponding vertex v in Gi+1. In this paper we studied the H-supermagic labelings of Dm(G) where G are paths and cycles.
Let G be a connected graph. Dominating set is a set of vertices which each vertex D has at least one neighbor in G. The minimum cardinality of D is called the domination number G(γ(G)). The metric ...dimension of G is the minimum cardinality of a series of vertices so that each vertex G is uniquely. It is determined by the distance of vector to the selected vertices. A dominating metric dimension set is a set of vertices has a dominating set D which has condition of metric dimension. The minimum cardinality is called the resolving domination number of G, (DomDim(G)). We analyze the resolving domination number of helm graph and it's operation. We study combine the existence concept of dominating set and metric dimension. We have obtained the minimum cardinality of dominating number.
Abstract
Let
G
be a connected, finite, and undirected graph. A vertex set
D
in
G
is an efficient dominating set of
G
if
D
is an independent set and for each point υ ∈
V
(
G
)-
D
is adjacent to ...precisely one vertex
d
∈
D.
The representation of points
υ
∈
V
(
G
) in respect of an ordered set
W
= {
w
1
,
w
2
,…,
w
k
} is the
k
–vector
r
(
υ
|
W
) = (
d
(
υ
,
w
1
),
d
(
υ
,
w
2
),…,
d
(
v, w
k
)), which
d
(
u, v
) is the distance between the points
u
and
υ
. The set W is a resolving set of
G
if
r
(
u
|
W
) =
r
(
υ
|
W
), for each point
u
and
υ
in
G
. A set of vertices in graph
G
which is an efficient dominating set and resolving set is called a resolving efficient dominating set. The minimal cardinality of resolving efficient dominating set is called resolving efficient domination number, denoted by
γ
re
(
G
). The comb product between graph
G
and graph
H
is a graph which get from taking a copy of graph
G
as many vertices of graph
H
and grafting the i-th copy of graph G to each vertex of H, and its notated by
G
▹
H
. In this paper, we determine the resolving efficient domination number of comb product graph, namely
K
n
▹
C
3
,
K
n
▹
P
3
,
W
n
▹
C
3
,
W
n
▹
P
3
, and
S
n
▹
P
2
Abstract
All graph in this paper is simple graph. Let G = (V, E) where V is nonempty of vertex set of G and E is possibly empty set of unordered pairs of elements of V. The distance from u to v in G ...is the lenght of a shortest path joining them, denoted by
d(u,v).
A function c : V (G) → {1,
2,…k}
is called a k-packing coloring if every c(u) = c(v) = i and
d(u,
v) > i + 1. The smallest positive integer of k which has packing coloring is packing chromatic number, denoted by χ
ρ
. In this paper, we investigated packing chromatic number of vertex amalgamation of some related tree graph, namely broom graph, star graph, path graph and banana graph.
Recently information technology has developed rapidly like the development of computer hardware and software. By the existence of internet technology, the process of data transfer can be done by ...others from a separate place and outside the system environment. The ease of data access remotely (using the internet) does not mean that they are always positive or good, but they also make new problems for the information world. The biggest problems when using the internet are slow access speeds and security when transferring data. Communication via internet is very susceptible to data loss or changed that caused by system errors or actions from non responsible persons. According to Kadir (2011) errors in data transfer via internet are caused by two reasons, that are the existence of human error or improper user intervention and the existence of technical errors from its system. Many efforts have been made by internet users to solve the problem of data transfer, including encoding data that will be sent in order to no user can read the data except the person has the right to receive it. Just not encoding, there is also an authentication process or validation of the data received, this is done to ensure that the data received is correct or does not changed. In this paper, the author propose a modification of the caesar cipher where if the key used previously is a real number, then we change the key into the coloring of vertices on the graph. So the key that used in this method is a graph. The core of this research is that every character of the plaintext has affiliation with each vertex of the graph, so that if the vertex of the graph gets 4 colors for example, then the characters of the plaintext affiliated with that vertex are also added with 4. This process will be repeated until all characters in the plaintext are coded according to the color of vertex. If the number of the characters plaintext is greater than the number of vertices, then the repeat process will occur until all the characters from the plaintext have affiliation with the vertex on the key graph.
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