The Hosoya index of a graph is defined as the total number of the matchings, including the empty edge set, of the graph. The Merrifield-Simmons index of a graph is defined as the total number of the independent vertex sets, including the empty vertex set, of the graph. Let U(n,∆) be the set of connected unicyclic graphs of order n with maximum degree ∆. We consider the Hosoya indices and the Me...

The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including some new versions of the indices): by cluster cardinality, by cluster weights, by inter-cluster edge/arc weights, by cluster element structure (for element m...

An octagon quadrangle is the graph consisting of an 8-cycle (x1, ..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X,B), where X is a finite set of v vertices and B is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKv defined on X. A 4-kite is the graph ha...

In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

a lot of research and various techniques have been devoted for finding the topologicaldescriptor wiener index, but most of them deal with only particular cases. there exist threeregular plane tessellations, composed of the same kind of regular polygons namely triangular,square, and hexagonal. using edge congestion-sum problem, we devise a method to computethe wiener index and demonstrate this m...

We present a theory of topological edge states in onedimensional resonant photonic crystals with compound unit cell. We demonstrate how the structure, despite being onedimensional, can be characterized by topological indices. Contrary to conventional electronic topological states the modes under consideration are radiative, i.e., they decay in time due to the light escape through the structure ...

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...