the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

The now well-known motion-silencing illusion has shown that salient changes among a group of objects' luminances, colors, shapes, or sizes may appear to cease when objects move rapidly (Suchow & Alvarez, 2011). It has been proposed that silencing derives from dot spacing that causes crowding, coherent changes in object color or size, and flicker frequencies combined with dot spacing (Choi, Bovi...

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a geodesic ~justifiable as long as the orbital evolution is adiabatic! we calculate numerically the fluxes of energy and angular momentum radiated to infinity and to ...

We consider generalizations of the k-source sum of vertex eccentricity problem (k-SVET) and the k-source sum of source eccentricity problem (k-SSET) [1], which we call SDET and SSET, respectively, and provide efficient algorithms for their solution. The SDET (SSET, resp.) problem is defined as follows: given a weighted graph G and sets S of source nodes and D of destination nodes, which are sub...

The eccentricity matrix of a connected graph $G$, denoted by $\mathcal{E}(G)$, is obtained from the distance $G$ keeping largest nonzero entries in each row and column leaving zeros remaining ones. $\mathcal{E}$-eigenvalues are eigenvalues $\mathcal{E}(G)$. modulus an eigenvalue $\mathcal{E}$-spectral radius $G$. $\mathcal{E}$-energy sum absolute values all In this article, we study some extrem...