Minimum Connected Dominating Sets of Random Cubic Graphs

Minimum independent dominating sets of random cubic graphs

We present a heuristic for finding a small independent dominating set, D, of cubic graphs. We analyse the performance of this heuristic, which is a random greedy algorithm, on random cubic graphs using differential equations and obtain an upper bound on the expected size of D. A corresponding lower bound is derived by means of a direct expectation argument. We prove that D asymptotically almost...

On connected k-domination in graphs

Let G = (V (G), E(G)) be a simple connected graph, and let k be a positive integer. A subset D ⊆ V (G) is a connected k-dominating set of G if its induced subgraph is connected and every vertex of V (G) −D is adjacent to at least k vertices of D. The connected k-domination number γ k(G) is the minimum cardinality among the connected k-dominating sets of G. In this paper, we give some properties...

TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS

Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...

Minimum Power Dominating Sets of Random Cubic Graphs

3 - Chromatic Cubic Graphs with Complementary Connected Domination Number Three

Let G (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex in V-S is adjacent to at least one vertex in S. The domination number γ (G) is the minimum cardinality taken over all such dominating sets in G. A subset S of V is said to be a complementary connected dominating set (ccd-set) if S is a dominating set and < V-S > is connected. The chromatic number χ is the m...