scholarly journals DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB

2019 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Fryda Arum Pratama ◽  
Liliek Susilowati ◽  
Moh. Imam Utoyo
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Metric Dimension ◽  
Star Graph ◽  
K Value ◽  
Product Graph ◽  
Path Graph ◽  
Dominating Number ◽  
Cycle Graph

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level  comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm). 

scholarly journals Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

2020 ◽  
Vol 1 (2) ◽  
pp. 64
Author(s):  
Nurma Ariska Sutardji ◽  
Liliek Susilowati ◽  
Utami Dyah Purwati
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Metric Dimension ◽  
Star Graph ◽  
Product Graph ◽  
Path Graph ◽  
Strong Metric Dimension ◽  
Metric Dimensions ◽  
Development Result ◽  
Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

The spectrum subgraph of the annihilating-ideal graph of a commutative ring

2015 ◽  
Vol 14 (08) ◽  
pp. 1550130
Author(s):  
R. Taheri ◽  
M. Behboodi ◽  
A. Tehranian
Keyword(s):  
Commutative Ring ◽  
Complete Graph ◽  
Connected Graph ◽  
Noetherian Ring ◽  
Prime Ideals ◽  
Star Graph ◽  
Induced Subgraph ◽  
Artinian Rings ◽  
Spectrum Graph

In this paper we introduce and study the spectrum graph of a commutative ring R, denoted by 𝔸𝔾s(R), that is, the graph whose vertices are all non-zero prime ideals of R with non-zero annihilator and two distinct vertices P1, P2 are adjacent if and only if P1P2 = (0). This is an induced subgraph of the annihilating-ideal graph 𝔸𝔾(R) of R. Among other results, we present the structures of all graphs which can be realized as the spectrum graph of a commutative ring. Then we show that for a non-domain Noetherian ring R, 𝔸𝔾s(R), is a connected graph if and only if 𝔸𝔾s(R) is a star graph if and only if 𝔸𝔾s(R) ≅ K1, K2 or K1,∞, where Kn is a complete graph with n vertices and K1,∞ is a star graph with infinite vertices. Also, we completely characterize the spectrum graphs of Artinian rings. Finally, as an application, we present some relationships between the annihilating-ideal graph and its spectrum subgraph.

scholarly journals Tadpole graphs and their laceability.

2021 ◽  
pp. 172-176
Keyword(s):  
Connected Graph ◽  
Hamiltonian Path ◽  
Path Graph ◽  
Cycle Graph

A connected graph G is termed Hamiltonian-t-laceable (t*-laceable) if there exists in G a Hamiltonian path between every pair (at least one pair) of its vertices u and v with the property d(u,v) = t. The Tadpole graph is the graph obtained by joining a cycle graph Cm to a path graph Pn with a bridge. In this paper, we discuss the laceability properties associated with the Tadpole graph.

scholarly journals Hubungan Dimensi Metrik Ketetanggaan dan Dimensi Metrik Ketetanggan Lokal Graf Hasil Operasi Kali Korona

2020 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Virdina Rahmayanti ◽  
Moh. Imam Utoyo ◽  
Liliek Susilowati
Keyword(s):  
Connected Graph ◽  
Basic Characteristic ◽  
Metric Dimension ◽  
Product Graph ◽  
Graph Operations ◽  
Trivial Graph ◽  
Corona Product

Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA(G⊙H), to determine the local adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA,l(G⊙H), and to determine the correlation between adjacency metric dimension and local adjacency metric dimension of corona product graph operations. In this research, it is found out that the value of adjacency metric dimension of G⊙H graph is affected by the basic characteristic of H and the domination characteristic. Meanwhile, the value of local adjacency metric dimension of G⊙H graph is only affected by the basic characteristic of H Futhermore, it is found a correlation of adjacency metric dimension and local adjacency metric dimension of corona product graph between any connected graph G and non-trivial graph H.

Bounds on the sum of domination number and metric dimension of graphs

2018 ◽  
Vol 10 (05) ◽  
pp. 1850066 ◽  
Author(s):  
Cong X. Kang ◽  
Eunjeong Yi
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
Domination Number ◽  
Unicyclic Graph ◽  
Metric Dimension ◽  
Minimum Cardinality ◽  
Dimension Formula ◽  
Vertex Set ◽  
Number Formula

Let [Formula: see text] be a graph with vertex set [Formula: see text]. The domination number, [Formula: see text], of [Formula: see text] is the minimum cardinality of a set [Formula: see text] such that every vertex not in [Formula: see text] is adjacent to a vertex in [Formula: see text]. The metric dimension, [Formula: see text], of [Formula: see text] is the minimum cardinality of a set of vertices such that every vertex of [Formula: see text] is uniquely determined by its vector of distances to the chosen vertices. For a tree [Formula: see text] of order at least two, we show that [Formula: see text], where [Formula: see text] denotes the number of exterior major vertices of [Formula: see text]; further, we characterize trees [Formula: see text] achieving equality. For a connected graph [Formula: see text] of order [Formula: see text], Bagheri Gh. et al. proved that [Formula: see text] and equality holds if and only if [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the complete graph and [Formula: see text] denotes a complete bi-partite graph of order [Formula: see text]. We characterize graphs [Formula: see text] for which [Formula: see text] equals two and three, respectively. We also characterize graphs [Formula: see text] satisfying [Formula: see text] when [Formula: see text] is a tree, a unicyclic graph, or a complete multi-partite graph.

scholarly journals ON STAR COLORING OF DEGREE SPLITTING OF COMB PRODUCT GRAPHS

2020 ◽  
pp. 507
Author(s):  
Ulagammal Subramanian ◽  
Vernold Vivin Joseph
Keyword(s):  
Chromatic Number ◽  
Complete Graph ◽  
Vertex Coloring ◽  
Star Graph ◽  
Path Graph ◽  
Product Graphs ◽  
Star Coloring ◽  
Splitting Graph ◽  
Proper Vertex

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.

scholarly journals Fuzzy square difference labeling of some graphs

10.26524/cm93 ◽  
2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Bharathi T ◽  
Jeya Rowena ◽  
Ashwini Sibiya Rani P
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Star Graph ◽  
Path Graph ◽  
Difference Graphs ◽  
Cycle Graph

We introduced a new concept called the Fuzzy square difference labeling. We proved that the path graph (Pn), the cycle graph (Cn), the star graph (Sn) and the complete bipartite graph (Km,n, n ≤ 3) are Fuzzy square difference graphs.

scholarly journals Tadpole graphs and their laceability.

2021 ◽  
pp. 393-397
Keyword(s):  
Connected Graph ◽  
Hamiltonian Path ◽  
Path Graph ◽  
Cycle Graph

A connected graph G is termed Hamiltonian-t-laceable (t*-laceable) if there exists in G a Hamiltonian path between every pair (at least one pair) of its vertices u and v with the property d(u,v) = t. The Tadpole graph is the graph obtained by joining a cycle graph Cm to a path graph Pn with a bridge. In this paper, we discuss the laceability properties associated with the Tadpole graph.

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