Gopalapillai,Indulal; Ivan,Gutman; Vijayakumar,Ambat(Department of Mathematics, August 25, 2007)
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Abstract:
The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the
D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are
said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds
for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular
D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.
The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the
D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are
said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds
for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular
D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.
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.
We define a new graph operator called the P3 intersection graph,
P3(G)- the intersection graph of all induced 3-paths in G. A characterization
of graphs G for which P-3 (G) is bipartite is given . Forbidden
subgraph characterization for P3 (G) having properties of being
chordal , H-free, complete are also obtained . For integers a and b
with a > 1 and b > a - 1, it is shown that there exists a graph G
such that X(G) = a, X(P3( G)) = b, where X is the chromatic number
of G. For the domination number -y(G), we construct graphs G such
that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1
and b. Similar construction for the independence number and radius,
diameter relations are also discussed.
Indulal,G; Vijayakumar,Ambat(Department of Mathematics, 2002)
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Abstract:
Two graphs G and H are Turker equivalent if they have the same set of Turker angles.
In this paper some Turker equivalent family of graphs are obtained.
The eigenvalue of a graph is the eigenvalue of its adjacency matrix . A graph
G is integral if all of its cigenvalues are integers. In this paper some new
classes of integral graphs are constructed.
In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property