in this paper, we determine the degree distance of the complement of arbitrary mycielskian graphs. it is well known that almost all graphs have diameter two. we determine this graphical invariant for the mycielskian of graphs with diameter two.

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...

Mahler’s measure is generalized to create the class of multiplicative distance functions. These functions measure the complexity of polynomials based on the location of their zeros in the complex plane. Following work of S.-J. Chern and J. Vaaler in [1], we associate to each multiplicative distance function two families of analytic functions which encode information about its range on C[x] and ...

In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...

In this paper, first we compute the energy of a special partitioned matrix under some cases. As consequence, obtain reciprocal distance complete multipartite graph and also give various other energies graphs. Next, show that among all [Formula: see text]-partite graphs on text] vertices, split has minimum is maximum for Turan text]. At last, it shown bipartite decreases deletion an edge if text...

The reciprocal complementary distance (RCD) matrix of a graphG is defined asRCD(G) = [rcij] where rcij = 1 1+D−dij if i 6= j and rcij = 0, otherwise, where D is the diameter of G and dij is the distance between the vertices vi and vj in G. The RCD-energy of G is defined as the sum of the absolute values of the eigenvalues of RCD(G). Two graphs are said to be RCDequienergetic if they have same R...