Siddani Bhaskara - Academia.edu (original) (raw)

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Papers by Siddani Bhaskara

this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G... more this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G2 are any two cographs, then there is a cograph that is both Eulerian and Hamiltonian having Gl as its median and G2 as its antimedian. Moreover, the connected planar and outer planar cographs are characterized and the median and antimedian graphs of connected, planar cographs are listed.

A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline... more A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline arrangement. We study the corresponding graph realization problem and properties of pseudoline arrangement graphs. In the first part, we give a simple criterion based on the degree sequence that says whether a degree sequence will have a pseudoline arrangement graph as one of its realizations. In the second part, we study the eccentricities of vertices in such graphs. We observe that the diameter (maximum eccentricity of a vertex in the graph) of any pseudoline arrangement graph on n pseudolines is n − 2. Then we characterize the diametrical vertices (whose eccentricity is equal to the graph diameter) of pseudoline arrangement graphs. These results hold for line arrangement graphs as well.

Journal of Combinatorial Theory, Series B, 1979

A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such t... more A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such that (i) G-S has more than I S I components, (ii) S induces the complete graph, and (iii) for every I(E S and v # S, we have do(u) > do(v), where do(u) denotes the degree of u in G. In this paper it is shown that a non-hamiltonian self-complementary graph G of order p is highly constricted, unless p = 4N and G is a particular graph G*(4N). It is also proved that if G is a se&complementary graph of order p(>8) and = its degree sequence, then G is pancyclic if r has a realization with a hamiltonian cycle, and G has a 2-factor if * has a realization with a 2-factor, unless p = 4N and G = G*(4N).

Arxiv preprint arXiv: …, 2010

In a digraph D = (X, U) , not necessarily finite, an arc (x, y) ∈ U is reachable from a vertex u ... more In a digraph D = (X, U) , not necessarily finite, an arc (x, y) ∈ U is reachable from a vertex u if there exists a directed walk W that originates from u and contains (x, y) . A subset S ⊆ X is an arc-reaching set of D if for every arc (x, y) there exists a diwalk W originating at a vertex u ...

this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G... more this paper, the median and the antimedian of cographs are discussed. It is shown that if G, and G2 are any two cographs, then there is a cograph that is both Eulerian and Hamiltonian having Gl as its median and G2 as its antimedian. Moreover, the connected planar and outer planar cographs are characterized and the median and antimedian graphs of connected, planar cographs are listed.

A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline... more A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline arrangement. We study the corresponding graph realization problem and properties of pseudoline arrangement graphs. In the first part, we give a simple criterion based on the degree sequence that says whether a degree sequence will have a pseudoline arrangement graph as one of its realizations. In the second part, we study the eccentricities of vertices in such graphs. We observe that the diameter (maximum eccentricity of a vertex in the graph) of any pseudoline arrangement graph on n pseudolines is n − 2. Then we characterize the diametrical vertices (whose eccentricity is equal to the graph diameter) of pseudoline arrangement graphs. These results hold for line arrangement graphs as well.

Journal of Combinatorial Theory, Series B, 1979

A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such t... more A graph G is said to be highly constricted if there exists a nonempty subset S of vertices such that (i) G-S has more than I S I components, (ii) S induces the complete graph, and (iii) for every I(E S and v # S, we have do(u) > do(v), where do(u) denotes the degree of u in G. In this paper it is shown that a non-hamiltonian self-complementary graph G of order p is highly constricted, unless p = 4N and G is a particular graph G*(4N). It is also proved that if G is a se&complementary graph of order p(>8) and = its degree sequence, then G is pancyclic if r has a realization with a hamiltonian cycle, and G has a 2-factor if * has a realization with a 2-factor, unless p = 4N and G = G*(4N).

Arxiv preprint arXiv: …, 2010

In a digraph D = (X, U) , not necessarily finite, an arc (x, y) ∈ U is reachable from a vertex u ... more In a digraph D = (X, U) , not necessarily finite, an arc (x, y) ∈ U is reachable from a vertex u if there exists a directed walk W that originates from u and contains (x, y) . A subset S ⊆ X is an arc-reaching set of D if for every arc (x, y) there exists a diwalk W originating at a vertex u ...