24 research outputs found
k-trees, k-ctrees and Line Splitting Graphs
Let G = (V,E) be a graph. For each edge ei of G, a new vertexe?i is taken and the resulting set of vertices is denoted by E1(G). Theline splitting graph Ls(G) of a graph G is defined as the graph havingvertex set E(G)SE1(G) with two vertices adjacent if they correspondto adjacent edges of G or one corresponds to an element e?i of E1(G)and the other to an element ej of E(G) where ej is in N(ei). In thispaper we characterize graphs whose line splitting graphs are k ? treesand k ? ctrees
Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs
For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G). The equality symbol '=' stands for on isomorphism between two graphs
Equitable total domination in graphs
A subset ܦ of a vertex set ܸሺܩሻ of a graph ܩ ൌ ሺܸ, ܧሻ is called an equitable dominating set if for every vertex ݒ א ܸ െ ܦ there exists a vertex ݑ א ܦ such that ݒݑ א ܧሺܩሻ and |݀݁݃ሺݑሻ െ ݀݁݃ሺݒሻ| 1, where ݀݁݃ሺݑሻ and ݀݁݃ሺݒሻ are denoted as the degree of a vertex ݑ and ݒ respectively. The equitable domination number of a graph ߛ ሺܩሻ of ܩ is the minimum cardinality of an equitable dominating set of .ܩ An equitable dominating set ܦ is said to be an equitable total dominating set if the induced subgraph ۄܦۃ has no isolated vertices. The equitable total domination number ߛ ௧ ሺܩሻ of ܩ is the minimum cardinality of an equitable total dominating set of .ܩ In this paper, we initiate a study on new domination parameter equitable total domination number of a graph, characterization is given for equitable total dominating set is minimal and also discussed Northaus-Gaddum type results
k-trees, k-ctrees and line splitting graphs
Let G = (V,E) be a graph. For each edge ei of G, a new vertexe?i is taken and the resulting set of vertices is denoted by E1(G). Theline splitting graph Ls(G) of a graph G is defined as the graph havingvertex set E(G)SE1(G) with two vertices adjacent if they correspondto adjacent edges of G or one corresponds to an element e?i of E1(G)and the other to an element ej of E(G) where ej is in N(ei). In thispaper we characterize graphs whose line splitting graphs are k ? treesand k ? ctrees
Characterizations of planar plick graphs
In this paper we present characterizations of graphs whose plick graphs are planar, outerplanar and minimally nonouterplanar
Integrity of Wheel Related Graphs
If a network modeled by a graph, then there are various graphtheoretical parameters used to express the vulnerability of communicationnetworks. One of them is the concept of integrity. In this paper, we determineexact values for the integrity of wheel related graphs
Multiplicative Zagreb indices and coindices of some derived graphs
In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph
Connected cototal domination number of a graph
A dominating set of a graph is said to be a connected cototal dominating set if is connected and , contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of is connected cototal dominating set. The connected cototal domination number of is the minimum cardinality of a minimal connected cototal dominating set of . In this paper, we begin an investigation of connected cototal domination number and obtain some interesting results