Papers by Mutharasu Sivagnanm
Iranian Journal of Mathematical Sciences and Informatics, 2014
Paul Erdos dened the concept of coprime graph and studied about cycles in coprime graphs. In this... more Paul Erdos dened the concept of coprime graph and studied about cycles in coprime graphs. In this paper this concept is generalized and a new graph called Generalized coprime graph is introduced. Having observed certain basic properties of the new graph it is proved that the chromatic number and the clique number of some generalized coprime graphs are equal.
Int. J. Open Problems Compt. Math, Jun 1, 2011
Cayley graph is a graph constructed out of a group Γ and a generating set A⊆ Γ. When Γ= Zn, the c... more Cayley graph is a graph constructed out of a group Γ and a generating set A⊆ Γ. When Γ= Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir (n, A). In this paper, we attempt to find the total domination number of Cir (n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir (n, A). Further, it is proved that Cir (n, A) is 2-total excellent if and only if n= t| A|+ 1 for some integer t> 0. Keywords: circulant graph, k-total excellent graph, total domination.
Mathematical Combinatorics, 2010
Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denot... more Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denoted by С (Γ, X). A Smarandachely n-Cayley graph is defined to be G= ZC (Γ, X), where V (G)= Γ× Zn and E (G)={((x, 0),(y, 1)) a,((x, 1),(y, 2)) a,···,((x, n− 2),(y, n− 1)) a: x, y∈ Γ, a∈ X such that y= x∗ a}. Particularly, a Smarandachely 2-Cayley graph is called as a Bi-Cayley graph, denoted by BС (Γ, X). Necessary and sufficient conditions for the existence of an efficient dominating set and an efficient open dominating set in Bi-Cayley graphs are ...
Abstract Cayley graph is a graph constructed out of a group Γ and a generating set A⊆ Γ. When Γ= ... more Abstract Cayley graph is a graph constructed out of a group Γ and a generating set A⊆ Γ. When Γ= Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir (n, A). In this paper, we attempt to find the total domination number of Cir (n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir (n, A). Further, it is proved that Cir (n, A) is 2-total excellent if and only if n= t| A|+ 1 for some integer t> 0. Keywords: circulant graph, k-total excellent graph, total domination.
Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denot... more Abstract: A Cayley graph is constructed out of a group Γ and its generating set X and it is denoted by С (Γ, X). A Smarandachely n-Cayley graph is defined to be G= ZC (Γ, X), where V (G)= Γ× Zn and E (G)={((x, 0),(y, 1)) a,((x, 1),(y, 2)) a,···,((x, n− 2),(y, n− 1)) a: x, y∈ Γ, a∈ X such that y= x∗ a}. Particularly, a Smarandachely 2-Cayley graph is called as a Bi-Cayley graph, denoted by BС (Γ, X).
Iranian Journal of Mathematical Sciences and Informatics, Nov 15, 2014
Paul Erdos defined the concept of coprime graph and studied about cycles in coprime graphs. In th... more Paul Erdos defined the concept of coprime graph and studied about cycles in coprime graphs. In this paper this concept is generalized and a new graph called Generalized coprime graph is introduced. Having observed certain basic properties of the new graph it is proved that the chromatic number and the clique number of some generalized coprime graphs are equal.
Uploads
Papers by Mutharasu Sivagnanm