scholarly journals Cordial Labeling of Corona Product of Path Graph and Second Power of Fan Graph

2021 ◽  
Vol 11 (02) ◽  
pp. 31-42
Author(s):  
Ashraf Ibrahim Hefnawy Elrokh ◽  
Shokry Ibrahim Mohamed Nada ◽  
Eman Mohamed El-Sayed El-Shafey
Keyword(s):  
Path Graph ◽  
Fan Graph ◽  
Corona Product

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 Eccentric Sequence of Graphs

2020 ◽  
Vol 8 (4S5) ◽  
pp. 52-54
Keyword(s):  
Cartesian Product ◽  
Undirected Graphs ◽  
Empty Graph ◽  
Path Graph ◽  
Ladder Graph ◽  
Fan Graph

The distance d(u, v) from a vertex u of graph G to a vertex v is the length of a shortest u to v path. The eccentric sequences were the first distance related sequences introduced for undirected graphs. The eccentricity e(v) of v is the distance of a farthest vertex from v. The eccentric sequence of a graph G is a list of the eccentricities of vertices of graph G arranged in non-decreasing order. In this paper we determine the eccentric sequence of join of an empty graph and path graph(ie fan graph) and the eccentric sequence of the Cartesian product of paths P2 and Pn (ie Ladder graph).

scholarly journals On local antimagic vertex coloring of corona products related to friendship and fan graph

2021 ◽  
Vol 5 (2) ◽  
pp. 110
Author(s):  
Zein Rasyid Himami ◽  
Denny Riama Silaban
Keyword(s):  
Chromatic Number ◽  
Connected Graph ◽  
Vertex Coloring ◽  
Antimagic Labeling ◽  
Minimum Number ◽  
Fan Graph ◽  
Corona Product

Let <em>G</em>=(<em>V</em>,<em>E</em>) be connected graph. A bijection <em>f </em>: <em>E</em> → {1,2,3,..., |<em>E</em>|} is a local antimagic of <em>G</em> if any adjacent vertices <em>u,v</em> ∈ <em>V</em> satisfies <em>w</em>(<em>u</em>)≠ <em>w</em>(<em>v</em>), where <em>w</em>(<em>u</em>)=∑<sub>e∈E(u) </sub><em>f</em>(<em>e</em>), <em>E</em>(<em>u</em>) is the set of edges incident to <em>u</em>. When vertex <em>u</em> is assigned the color <em>w</em>(<em>u</em>), we called it a local antimagic vertex coloring of <em>G</em>. A local antimagic chromatic number of <em>G</em>, denoted by <em>χ</em><sub>la</sub>(<em>G</em>), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of <em>G</em>. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on <em>m</em> vertices, namely, <em>χ</em><sub>la</sub>(<em>F</em><sub>n</sub> ⊙ \overline{K_m}) and <em>χ</em><sub>la</sub>(<em>f</em><sub>(1,n)</sub> ⊙ \overline{K_m}).

scholarly journals IMPLEMENTASI ALGORITMA MODIFIKASI BROYDEN-FLETCHER-GOLDFARB-SHANNO (MBFGS)

2017 ◽  
Vol 4 (5) ◽  
Author(s):  
Rahmawati Erma Standsyah
Keyword(s):  
Metric Dimension ◽  
Combinatorial Search ◽  
Robotic Navigation ◽  
Resolving Set ◽  
Circle Graph ◽  
Path Graph ◽  
Corona Product

The concept of minimum resolving set has proved to be useful and or related to a variety of fields such as Chemistry, Robotic Navigation, and Combinatorial Search and Optimization. Two graph are path graph (𝑃𝑛) anf circle graph (𝐶𝑚). The corona product 𝑃𝑛 ⨀𝐶𝑚 is defined as the graph obtained from 𝑃𝑛and 𝐶𝑚 by taking one copi of 𝑃𝑛 and 𝑚1copies of 𝐶𝑚 and joining by an edge each vertex from the 𝑛𝑡ℎ copy of 𝑃𝑛 with the 𝑚𝑡ℎ vertex of 𝐶𝑚. 𝑃𝑛 ⨀ 𝐶𝑚 and 𝐶𝑚⨀𝑃𝑛 not commute to 𝑛≠𝑚, it is showed that order of graph 𝑃𝑛 ⨀ 𝐶𝑚 different with graph 𝐶𝑚⨀𝑃𝑛. Based on research obtained 𝑑𝑖𝑚(𝑃𝑛⨀𝐶𝑚)=𝑛.𝑑𝑖𝑚(𝑊1,𝑚) dan 𝑑𝑖𝑚(𝐶𝑚⨀𝑃𝑛)=𝑚.𝑑𝑖𝑚 (𝐾1+𝑃𝑛)Keyword : Resolving Sets, Metric Dimension, Path Graph, Circle Graph, Corona Graph

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