Strong open geodetic number

2020 ◽  
Author(s):  
Deepa Mathew ◽  
S. Arul Amirtha Raja ◽  
Eddith Sarah Varghese ◽  
D. Antony Xavier
Keyword(s):  
Geodetic Number

scholarly journals Algorithmic upper bounds for graph geodetic number

2021 ◽  
Author(s):  
Ahmad T. Anaqreh ◽  
Boglárka G.-Tóth ◽  
Tamás Vinkó
Keyword(s):  
Upper Bounds ◽  
Geodetic Number

scholarly journals The 2-edge geodetic number and graph operations

2012 ◽  
Vol 1 (2) ◽  
pp. 241-249 ◽  
Author(s):  
A. P. Santhakumaran ◽  
S. V. Ullas Chandran
Keyword(s):  
Graph Operations ◽  
Geodetic Number

scholarly journals The edge geodetic self decomposition number of a graph

2020 ◽  
Author(s):  
John J ◽  
Stalin D
Keyword(s):  
Connected Graph ◽  
Maximum Cardinality ◽  
Connected Graphs ◽  
Edge Disjoint ◽  
General Properties ◽  
Geodetic Number ◽  
Simple Connected Graph ◽  
Decomposition Number

Let  G = (V, E)  be a simple connected  graph  of order  p and  size q.  A decomposition  of a graph  G is a collection  π  of edge-disjoint sub graphs  G1, G2, ..., Gn  of G such  that every  edge of G belongs to exactly  one Gi , (1 ≤ i ≤ n) . The decomposition  π = {G1, G2, ....Gn } of a connected  graph  G is said to be an edge geodetic self decomposi- tion  if ge (Gi ) = ge (G), (1 ≤ i ≤ n).The maximum  cardinality of π is called the edge geodetic self decomposition  number of G and is denoted by πsge (G), where ge (G) is the edge geodetic number  of G.  Some general properties   satisfied  by  this  concept  are  studied.    Connected  graphs which are edge geodetic self decomposable  are characterized.

The geodetic number of the lexicographic product of graphs

2011 ◽  
Vol 311 (16) ◽  
pp. 1693-1698 ◽  
Author(s):  
Boštjan Brešar ◽  
Tadeja Kraner Šumenjak ◽  
Aleksandra Tepeh
Keyword(s):  
Lexicographic Product ◽  
Geodetic Number ◽  
Product Of Graphs

scholarly journals The upper edge geodetic number and the forcing edge geodetic number of a graph

2009 ◽  
Vol 29 (4) ◽  
pp. 427 ◽  
Author(s):  
A. P. Santhakumaran ◽  
J. John
Keyword(s):  
Geodetic Number

scholarly journals THE FORCING EDGE-TO-VERTEX GEODETIC NUMBER OF A GRAPH

2015 ◽  
Vol 103 (1) ◽  
Author(s):  
S. Sujitha ◽  
J. John ◽  
A. Vijayan
Keyword(s):  
Geodetic Number

scholarly journals Forcing Total Outer Independent Edge Geodetic Number of a Graph

2021 ◽  
Vol 1947 (1) ◽  
pp. 012021
Author(s):  
P. Arul Paul Sudhahar ◽  
A. Ajin Deepa
Keyword(s):  
Geodetic Number ◽  
Independent Edge

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).

scholarly journals Graphs with large geodetic number

Filomat ◽  
2015 ◽  
Vol 29 (6) ◽  
pp. 1361-1368 ◽  
Author(s):  
Hossein Ahangar Abdollahzadeh ◽  
Saeed Kosari ◽  
Seyed Sheikholeslami ◽  
Lutz Volkmann
Keyword(s):  
Geodetic Number
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