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 $...

Multi-attribute decision making (MADM) play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, interval neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on interval neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation (INTrLWAA) operator and interval...

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some estimates of Hermite–Hadamard inequalities for integrals. The results presented in paper are generalizations comparable literature on inequalities. Several inequalities, such as midpoint-like inequality, Simpson-like averaged midpoint–trapezoid-like and trapezoid-like obtained special cases ...

Tolerance graphs have been extensively studied since their introduction, due to their interesting structure and their numerous applications, as they generalize both interval and permutation graphs in a natural way. It has been conjectured by Golumbic, Monma, and Trotter in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocompara...

Actin stress fibers (SFs) of cells cultured on cyclically stretched substrate tend to reorient in the direction in which a normal strain of substrate becomes zero. However, little is known about the mechanism of this reorientation. Here we investigated the effects of cyclic stretch waveform on SF reorientation in osteoblastic cells. Cells adhering to silicone membranes were subjected to cyclic ...

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.

In the symmetric and the asymmetric trapezoid maps, as a slope a of the trapezoid is increased, the period doubling cascade occurs and the symbolic sequence of periodic points is the Metropolis-Stein-Stein sequence R∗m and the convergence of the onset point am of the period 2 m solution to the accumulation point ac is exponentially fast. In the previous paper, we proved these results. In this p...

Let G be a graph. A component of G is a maximal connected subgraph in G. A vertex v is a cut vertex of G if κ(G− v) > κ(G), where κ(G) is the number of components in G. Similarly, an edge e is a bridge of G if κ(G− e) > κ(G). In this paper, we will propose new O(n) algorithms for finding cut vertices and bridges of a trapezoid graph, assuming the trapezoid diagram is given. Our algorithms can b...