scholarly journals Domination and Eternal Domination of Jahangir Graph

2019 ◽  
Vol 09 (03) ◽  
pp. 68-81
Author(s):  
Ramy Shaheen ◽  
Mohammad Assaad ◽  
Ali Kassem
Keyword(s):  
Jahangir Graph

scholarly journals Super (a, d)-Cycle-Antimagic Total Labeling on Triangular Ladder Graph and Generalized Jahangir Graph

2017 ◽  
Vol 855 ◽  
pp. 012037
Author(s):  
Mania Roswitha ◽  
Anna Amanda ◽  
Titin Sri Martini ◽  
Bowo Winarno
Keyword(s):  
Ladder Graph ◽  
Jahangir Graph

scholarly journals On Eternal Domination of Generalized J s , m

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ramy Shaheen ◽  
Mohammad Assaad ◽  
Ali Kassem
Keyword(s):  
Infinite Series ◽  
Dominating Set ◽  
Domination Number ◽  
Adjacent Vertex ◽  
Dominating Set Problem ◽  
Jahangir Graph ◽  
Domination Numbers

An eternal dominating set of a graph G is a set of guards distributed on the vertices of a dominating set so that each vertex can be occupied by one guard only. These guards can defend any infinite series of attacks, an attack is defended by moving one guard along an edge from its position to the attacked vertex. We consider the “all guards move” of the eternal dominating set problem, in which one guard has to move to the attacked vertex, and all the remaining guards are allowed to move to an adjacent vertex or stay in their current positions after each attack in order to form a dominating set on the graph and at each step can be moved after each attack. The “all guards move model” is called the m -eternal domination model. The size of the smallest m -eternal dominating set is called the m -eternal domination number and is denoted by γ m ∞ G . In this paper, we find the domination number of Jahangir graph J s , m for s ≡ 1 , 2   mod   3 , and the m -eternal domination numbers of J s , m for s , m are arbitraries.

scholarly journals The Vertex Prime Valuation for Jahangir and Theta Graphs

2019 ◽  
Vol 8 (12) ◽  
pp. 5019-5021
Keyword(s):  
Disjoint Union ◽  
Graph Operations ◽  
Jahangir Graph

A sequence of instructions which can help to solve a problem is called an algorithm. The reason for composing an algorithm is to reduce the timespan and understanding the solution of problems in simple way. In this paper, vertex prime valuation of the Jahangir graph Jn,m for n ≥ 2, m ≥ 3 and generalized Theta graph θ (l1 , l 2 , l 3 , ..., ln) has been investigated by using algorithms .We discuss vertex prime valuation of some graph operations on both graphs viz. Fusion, Switching and Duplication, Disjoint union and Path union.

scholarly journals Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Ramy Shaheen ◽  
Ziad Kanaya ◽  
Khaled Alshehada
Keyword(s):  
Chromatic Number ◽  
Proper Coloring ◽  
Game Chromatic Number ◽  
Generalized Petersen Graphs ◽  
Minimum Number ◽  
Petersen Graphs ◽  
Jahangir Graph ◽  
Prism Graph

Let G = V , E be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph G a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by χ g G , while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number χ g G of Generalized Petersen Graphs G P n , k for k ≥ 3 and arbitrary n , n -Crossed Prism Graph, and Jahangir Graph J n , m .

scholarly journals The eccentric digraph of caterpillar graph and generalized Jahangir graph

2021 ◽  
Author(s):  
Tri Atmojo Kusmayadi ◽  
Nugroho Arif Sudibyo
Keyword(s):  
Jahangir Graph

A study of newly defined degree-based topological indices via M-polynomial of Jahangir graph

2021 ◽  
Vol 24 (2) ◽  
pp. 427-438
Author(s):  
Deeba Afzal ◽  
Samia Ali ◽  
Farkhanda Afzal ◽  
Murat Cancan ◽  
Süleyman Ediz ◽  
...  
Keyword(s):  
Topological Indices ◽  
Jahangir Graph

scholarly journals COMPUTATION OF TOPOLOGICAL INDICES OF LINE GRAPH OF JAHANGIR GRAPH

2018 ◽  
Vol 8 (2) ◽  
pp. 91-107
Author(s):  
Mehdi Alaeiyan ◽  
◽  
Muhammad S. Sardar ◽  
Sohail Zafar ◽  
Zohaib Zahid ◽  
...  
Keyword(s):  
Line Graph ◽  
Topological Indices ◽  
Jahangir Graph

scholarly journals Prime Labeling of Jahangir Graphs

2018 ◽  
Vol 7 (4.10) ◽  
pp. 389
Author(s):  
Anantha Lakshmi. ◽  
Jayalakshmi. K ◽  
Madhavi T
Keyword(s):  
Prime Number ◽  
Prime Graph ◽  
Graph Operations ◽  
Prime Labeling ◽  
Jahangir Graph

The paper investigates prime labeling of Jahangir graph Jn,m   for n ≥ 2, m ≥ 3 provided that nm is even. We discuss prime labeling of some graph operations viz. Fusion, Switching and Duplication to prove that the Fusion of two vertices v1 and vk where k is odd in a Jahangir graph Jn,m results to prime graph provided that the product nm is even and is relatively prime to k. The Fusion of two vertices vnm + 1 and vk for any k in Jn, m is prime. The switching of vk in the cycle Cnm of the Jahangir graph Jn,m  is a prime graph provided that nm+1 is a prime number and the switching of vnm+1 in Jn, m is also a prime graph .Duplicating of vk, where k is odd integer and nm + 2 is relatively prime to k,k+2 in Jn,m is a prime graph.  

Sign in / Sign up

Export Citation Format

Share Document