# Majority Domatic Number - I

## Related Articles

- ON THE TOTAL RESTRAINED DOMINATION NUMBER OF DIRECT PRODUCTS OF GRAPHS. WAI CHEE SHIU; HONG-YU CHEN; XUE-GANG CHEN; PAK KIU SUN // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p629
Let G = (V,E) be a graph. A total restrained dominating set is a set S âŠ† V where every vertex in V \ S is adjacent to a vertex in S as well as to another vertex in V \ S, and every vertex in S is adjacent to another vertext in S. The total restrained domination number of G, denoted by...

- DOUBLE DOMINATION CRITICAL AND STABLE GRAPHS UPON VERTEX REMOVAL. KHELIFI, SOUFIANE; CHELLALI, MUSTAPHA // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p643
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number of G, denoted Î³x2(G), is the minimum cardinality among all double dominating sets of...

- TREES WITH EQUAL 2-DOMINATION AND 2-INDEPENDENCE NUMBERS. Chellali, Mustapha; Meddah, Nacéra // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p263
Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V - S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number Î³2(G)...

- THE i-CHORDS OF CYCLES AND PATHS. MCKEE, TERRY A. // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p607
An i-chord of a cycle or path is an edge whose endpoints are a distance i â‰¥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results...

- Graph Equation for Line Graphs and m-Step Graphs. Kim, Seog-Jin; Kim, Suh-Ryung; Lee, Jung; Park, Won; Sano, Yoshio // Graphs & Combinatorics;Nov2012, Vol. 28 Issue 6, p831
Given a graph G, the m-step graph of G, denoted by S( G), has the same vertex set as G and an edge between two distinct vertices u and v if there is a walk of length m from u to v. The line graph of G, denoted by L( G), is a graph such that the vertex set of L( G) is the edge set of G and two...

- 3-TRANSITIVE DIGRAPHS. Hernández-Cruz, César // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 3, p205
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are...

- SOME RESULTS ON SEMI-TOTAL SIGNED GRAPHS. SINHA, DEEPA; GARG, PRAVIN // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 4, p625
A signed graph (or sigraph in short) is an ordered pair S = (SuÎ´), where Su is a graph G = (V,E), called the underlying graph of S and Î´ : E â†’ {+,-} is a function from the edge set E of Suinto the set {+,-}, called the signature of S. The x-line sigraph of S denoted by L x (S) is a...

- Paired-Domination in P 5-Free Graphs. Dorbec, Paul; Gravier, Sylvain // Graphs & Combinatorics;Nov2008, Vol. 24 Issue 4, p303
A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by $$\gamma_pr(G)$$ , is the minimum cardinality of a paired-dominating...

- Domination polynomials of cubic graphs of order 10. Alikhani, Saeid; Yee-Hock Peng // Turkish Journal of Mathematics;2011, Vol. 35 Issue 3, p355
Let G be a simple graph of order n. The domination polynomial of G is the polynomial Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where d(G, i) is the number of dominating sets of G of size i, and Î³(G) is the domination number of G. In this...