The (t) property of some classes of graphs

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

Studies on Fuzzy Graphs

In this thesis an attempt to develop the properties of basic concepts in fuzzy graphs such as fuzzy bridges, fuzzy cutnodes, fuzzy trees and blocks in fuzzy graphs have been made. The notion of complement of a fuzzy graph is modified and some of its properties are studied. Since the notion of complement has just been initiated, several properties of G and G available for crisp graphs can be studied for fuzzy graphs also. Mainly focused on fuzzy trees defined by Rosenfeld in [10] , several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. It is observed that there are selfcentered fuzzy trees. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. The study of fuzzy graphs made in this thesis is far from being complete. The wide ranging applications of graph theory and the interdisciplinary nature of fuzzy set theory, if properly blended together could pave a way for a substantial growth of fuzzy graph theory.

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

On Distance Energy of Graphs

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.

A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

Equienergetic self-complementary graphs

In this paper equienergetic self-complementary graphs on p vertices for every p = 4k; k ¸ 2 and p = 24t + 1; t ¸ 3 are constructed

Some classes of Turker equivalent graphs

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.

Simple Low-cost Planar Antenna for Indoor Communication under the Bluetooth Protocol

A single-feed rectangular-ring microstrip antenna is proposed for indoor communication under the Bluetooth protocol. The dimensions of the antenna together with the location of the feed point are optimized through field simulations in order to cover the Bluetooth bandwidth and to avoid linear polarization. The performance and the efficiency of the antenna are illustrated in a real indoor environment

Compact Planar Multiband Antenna for GPS, DCS, 2.4/5.8 GHz WLAN Applications

A compact single –feed multiband planar antenna configuration Suitable for GPS, DCS. 2.4/5.8 GHz WLAN applications are presented. The antenna has dimensions 38 x 3 x 1.6 mm and offers good radiation and reflection characteristics in the above frequency bands. The antenna has a simple geometry and can be easily fed using a 50 coaxial probe

Planar L-strip FED Broadband Microstrip Antenna

A broadband rectangular tnicrostrip antenna utilizing an electromagnetically coupled L-strip feed is presented. Experimental study shows a 2:1 VSWR bandwidth of a 10% and excellent cross-polarization performance with a radiation coverage almost as same as that of the rectangular microstrip antenna fed by conventional methods. The variation of bandwidth for different feed parameters is also studied. The proposed antenna is suitable for broadband communications

Rectangular Dielectric Resonator Antenna on a Conductor-backed Co-planar

In this paper, we present an effective excitation of a reelangular dielectric resonator antennas (DRA) with a conductor-hacked coplanar waveguide (CB-CPW). The radiation and resonance characteristics are found to van,, depending on the orientation of the DR on doe coplanar feed line. The effect of finite and infinite ground planes of CB-CPIV on the radiation characteristics of the rectangular DRA is studied. The orientation and position of the DR are optimized for maximum gain and bandwidth. The optimized antenna ,geometry offers --10.46 dBi gain and 7.5% bandwidth with low cross-polar radiation characteristics

SOME NEW INTEGRAL GRAPHS

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.

ON THE MEDIAN AND THE ANTIMEDIAN OF A COGRAPH

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.

ON DISTANCE ENERGY OF GRAPHS

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.

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.