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