scholarly journals Minimal Total Dominating Functions of Corona Product Graph of a Cycle with a Complete Graph

2014 ◽  
Vol 6 (8) ◽  
pp. 11-16
Author(s):  
M. SivaParvathi ◽  
B. Maheswari
Keyword(s):  
Complete Graph ◽  
Product 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.

On a Conjecture of Bollobás and Brightwell Concerning Random Walks on Product Graphs

1998 ◽  
Vol 7 (4) ◽  
pp. 397-401 ◽  
Author(s):  
OLLE HÄGGSTRÖM
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Discrete Time ◽  
Complete Graph ◽  
Continuous Time ◽  
Product Graph ◽  
Product Graphs ◽  
Continuous Time Random Walks ◽  
Discrete Time Case

We consider continuous time random walks on a product graph G×H, where G is arbitrary and H consists of two vertices x and y linked by an edge. For any t>0 and any a, b∈V(G), we show that the random walk starting at (a, x) is more likely to have hit (b, x) than (b, y) by time t. This contrasts with the discrete time case and proves a conjecture of Bollobás and Brightwell. We also generalize the result to cases where H is either a complete graph on n vertices or a cycle on n vertices.

scholarly journals Unidominating Functions of Corona Product Graph

2019 ◽  
Vol 177 (15) ◽  
pp. 44-47
Author(s):  
B. Aruna ◽  
B. Maheswari
Keyword(s):  
Product Graph ◽  
Corona Product

scholarly journals Analogies between the geodetic number and the Steiner number of some classes of graphs

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1781-1788 ◽  
Author(s):  
Ismael Yero ◽  
Juan Rodríguez-Velázquez
Keyword(s):  
Complete Graph ◽  
Open Problem ◽  
Minimum Size ◽  
Discrete Mathematics ◽  
Connected Subgraph ◽  
Minimum Cardinality ◽  
Geodetic Number ◽  
Product Graphs ◽  
Geodetic Set ◽  
Corona Product

A set of vertices S of a graph G is a geodetic set of G if every vertex v ? S lies on a shortest path between two vertices of S. The minimum cardinality of a geodetic set of G is the geodetic number of G and it is denoted by 1(G). A Steiner set of G is a set of vertices W of G such that every vertex of G belongs to the set of vertices of a connected subgraph of minimum size containing the vertices of W. The minimum cardinality of a Steiner set of G is the Steiner number of G and it is denoted by s(G). Let G and H be two graphs and let n be the order of G. The corona product G ? H is defined as the graph obtained from G and H by taking one copy of G and n copies of H and joining by an edge each vertex from the ith-copy of H to the ith-vertex of G. We study the geodetic number and the Steiner number of corona product graphs. We show that if G is a connected graph of order n ? 2 and H is a non complete graph, then g(G ? H) ? s(G ? H), which partially solve the open problem presented in [Discrete Mathematics 280 (2004) 259-263] related to characterize families of graphs G satisfying that g(G) ? s(G).

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