In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integerm. Ifm > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 + m2,m4 + m2,m4 + m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defi...

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 ...

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integerm. Ifm > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 + m2,m4 + m2,m4 + m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defi...

We say that a regular graph G of order n and degree r ? 1 (which is not the complete graph) strongly if there exist non-negative integers such |Si Sj | = for any two adjacent vertices i j, distinct non-adjacent where Sk denotes neighborhood vertex k. Let ?1 r, ?2 ?3 be eigenvalues connected graph. m1 1, m2 m3 denote multiplicity ?3, respectively. here describe parameters n, graphs with qm3 qm2 ...

Let G be a graph of order n with (0, 1)-adjacency matrix A. An eigenvalue σ of A is said to be an eigenvalue of G, and σ is a main eigenvalue if the eigenspace EA(σ) is not orthogonal to the all-1 vector in IR. Always the largest eigenvalue, or index, of G is a main eigenvalue, and it is the only main eigenvalue if and only if G is regular. We say that G is an integral graph if every eigenvalue...

Recently Friedman proved Alon’s conjecture for many families of d-regular graphs, namely that given any 2 > 0 “most” graphs have their largest non-trivial eigenvalue at most 2 √ d− 1+ 2 in absolute value; if the absolute value of the largest non-trivial eigenvalue is at most 2 √ d− 1 then the graph is said to be Ramanujan. These graphs have important applications in communication network theory...

Recently, Huang showed that every ( 2 n − 1 + ) -vertex induced subgraph of the n-dimensional hypercube has maximum degree at least . In this paper, we discuss subgraphs Cartesian product graphs and semistrong to generalize Huang's result. Let Γ be a connected signed bipartite graph order m. By defining two kinds , denoted by □ ˜ ⋈ show if have exactly distinct adjacency eigenvalues ± θ respect...