let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

By a symmetric graph we mean a graph X which automorphism group acts transitively on the arcs of X. A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. Tutte [31, 32] showed that every finite symmetric cubic graph is s-regular for some s ≤ 5. It is well-known that there are precisely five symmetric cubic graphs of girth less than 6. All these graphs can be re...

Abstract. Error fields and resistive magnetohydrodynamic (MHD) modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. The broken toroidal symmetry leads to enhanced neoclassical toroidal plasma viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal plasma viscosity also results in a steady s...

The Hom complex of homomorphisms between two graphs was originally introduced to provide topological lower bounds on the chromatic number of graphs. In this paper we introduce new methods for understanding the topology of Hom complexes, mostly in the context of Γ-actions on graphs and posets (for some group Γ). We view the Hom(T, •) and Hom(•, G) as functors from graphs to posets, and introduce...

a graph that contains a hamiltonian cycle is called a hamiltonian graph. in this paper wecompute the first and the second geometric – arithmetic indices of hamiltonian graphs. thenwe apply our results to obtain some bounds for fullerene.

a connected graph g is said to be neighbourly irregular graph if no two adjacent vertices of g have same degree. in this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.

We study the strict majority bootstrap percolation process on graphs. Vertices may be active or passive. Initially, active vertices are chosen independently with probability p. Each passive vertex v becomes active if at least d deg(v)+1 2 e of its neighbors are active (and thereafter never changes its state). If at the end of the process all vertices become active then we say that the initial s...

An r-dynamic proper k-coloring of a graph G is a proper k-coloring of G such that every vertex in V (G) has neighbors in at least min{d(v), r} different color classes. The r-dynamic chromatic number of a graph G, written χr(G), is the least k such that G has such a coloring. By a greedy coloring algorithm, χr(G) ≤ r∆(G) + 1; we prove that equality holds for ∆(G) > 2 if and only if G is r-regula...

The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristic...

Theories for the toroidal momentum confinement in tokamaks have been developed. It is shown that the logarithmic gradient of the toroidal flow is a linear combination of logarithmic gradients of the plasma pressure and the temperature in neoclassical quasilinear theory. The fluctuation-induced toroidal stress consists of a diffusion flux, a convective flux, and a residual flux. The effects of a...