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2. Domination numbers on the complement of the Boolean function graph of a graph
- Creator:
- Janakiraman, T. N., Muthammai, S., and Bhanumathi, M.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- domination number, eccentricity, radius, diameter, neighborhood, perfect matching, and Boolean function graph
- Language:
- English
- Description:
- For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G), NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G), NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is denoted by B1(G). In this paper, we determine domination number, independent, connected, total, point-set, restrained, split and non-split domination numbers in the complement B1(G) of B1(G) and obtain bounds for the above numbers.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. Graphs with the same peripheral and center eccentric vertices
- Creator:
- Kyš, Peter
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- graph, radius, diameter, center, eccentricity, and distance
- Language:
- English
- Description:
- The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v, and u is an eccentric vertex for v if its distance from v is d(u, v) = e(v). A vertex of maximum eccentricity in a graph G is called peripheral, and the set of all such vertices is the peripherian, denoted PeriG). We use Cep(G) to denote the set of eccentric vertices of vertices in C(G). A graph G is called an S-graph if Cep(G) = Peri(G). In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of • S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. On the Boolean function graph of a graph and on its complement
- Creator:
- Janakiraman, T. N., Muthammai, S., and Bhanumathi, M.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- eccentricity, self-centered graph, middle graph, and Boolean function graph
- Language:
- English
- Description:
- For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G), NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G), NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is denoted by B1(G). In this paper, structural properties of B1(G) and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public