It is proved that a compact Kähler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kähler–Einstein manifolds. A stronger result is established for the case of Kähler surfaces. Without the compactness assumption, irreducible Kähler manifolds with Ricci tensor having two distinct constant eigenvalues are shown to exist in various situat...

In this paper, we investigate the relation between the Q -spectrum and the structure of G in terms of the circumference of G. Exploiting this relation, we give a novel necessary condition for a graph to be Hamiltonian by means of its Q -spectrum. We also determine the graphs with exactly one or two Q -eigenvalues greater than or equal to 2 and obtain all minimal forbidden subgraphs and maximal ...

Algebraic combinatorics is the area of mathematics that uses the theories and methods of abstract and linear algebra to solve combinatorial problems, or conversely applies combinatorial techniques to solve problems in algebra. In particular, spectral graph theory applies the techniques of linear algebra to study graph theory. Spectral graph theory is the study of the eigenvalues of various matr...

The eccentricity matrix E(G) of a connected graph G is obtained from the distance by keeping largest nonzero entries in each row and column, leaving zeros remaining ones. eigenvalues are E-eigenvalues G. In this article, we find inertia matrices trees. Interestingly, any tree on more than 4 vertices with odd diameter has exactly two positive negative (irrespective structure tree). Also, show th...

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

A graph Γ with diameter d is strongly distance-regular if Γ is distanceregular and its distance-d graph Γd is strongly regular. The known examples are all the connected strongly regular graphs (i.e. d = 2), all the antipodal distanceregular graphs, and some distance-regular graphs with diameter d = 3. The main result in this paper is a characterization of these graphs (among regular graphs with...

the eigenvalues of a graph is the root of its characteristic polynomial. a fullerene f is a 3-connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n isthe number of vertices of f. in this paper we investigate the eigenvalues of a class of fullerenegraphs.

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m for every positive integer m. If m > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m, 2m +m, m +m, m +m). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by ...