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 $...

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...

The limits of a recently proposed computer method for finding all distinct substructures of a chemical structure are systematically explored within comprehensive graph samples which serve as supersets of the graphs corresponding to saturated hydrocarbons, both acyclic (up to n = 20) and (poly)cyclic (up to n = 10). Several pairs of smallest graphs and compounds are identified that cannot be dis...

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.

[reaction: see text] This Letter describes the synthesis of the hemibrevetoxin B tetracyclic ring system in 14 linear transformations from the Danishefsky-Kitahara diene.

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 ...

Two high-yielding strategies for the synthesis of 4H-anthra[1,2-b]pyran antibiotics have been developed giving access to novel antitumor agent (ED(50) 1.5 microm) and to (S)-espicufolin (3). A key step for the assembly of the tetracyclic 4H-anthra[1,2-b]pyran-4,7,12-trione skeleton is the nucleophilic addition of an aryl lithium species onto an aldehyde which allows the introduction of either a...

Highly strained biarylazacyclooctynone (BARAC) and analogous bioconjugation reagents were shown to undergo novel rearrangement and addition reactions leading to tetracyclic products. This may limit their practical applicability as bioorthogonal reporters for imaging biomolecules within living systems.