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.

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of “rank-homogeneous” trees. We consider these conditions as a possible definition of what it means for a class of structures to have “Ulm type”. The result says that there can be no Turing computable embedding o...

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of “rank-homogeneous” trees. We consider these conditions as a possible definition of what it means for a class of structures to have “Ulm type”. The result says that there can be no Turing computable embedding o...

The testicular torsion which is typically seen in prepuberty is very rare in the early neonatal period; prenatal diagnosis is difficult. Herein, we report a five day-old male neonate with swelling and erythema of the right scrotum.  Following Doppler ultrasound suggestive of testicular torsion, surgical exploration was undertaken. There was gangrene of the right testis with discoloration and ne...

The exchange graph of a quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchange graph. Building on work of Iyama, Reiten, Thomas, and Todorov, we show that this directed graph is a semidistributive lattice by using the isomorphism to the lattice of functorially finite torsion cla...

The directed power graph $$\vec {\mathcal {G}}( G)$$ of a group G is the simple digraph with vertex set in which $$x\rightarrow y$$ if y x, and underlying $$\mathcal {G}( . In this paper, three versions definition are discussed, it proved that by any determines other two up to isomorphism. It also torsion-free nilpotency class 2 H such H)\cong \mathcal , then have isomorphic graphs, was an open...

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

introduction left ventricular (lv) twist is believed to store potential energy and plays an important role in generating diastolic suction. recent advances in echocardiography techniques have allowed quantification of lv twist. the aim of the present study was to compare lv twist and torsion in healthy human subjects determined by velocity vector imaging (vvi) and tissue doppler imaging (tdi) a...