In a 1967 paper, Banchoff described a theory of critical points and curvature for polyhedra embedded in Euclidean space. For each convex cell complex K in Rn, and for each linear map h : Rn ! R satisfying a simple generality criterion, he defined an index for each vertex of K with respect to the map h, and showed that these indices satisfy two properties: (1) for each map h, the sum of the indi...

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

The study of topological indices in graph theory is one the more important topics, as scientific development that occurred previous century had an impact by linking it to many chemical and physical properties such boiling point melting point. So, our interest this paper “generalized indices’ network” for some graphs have somewhat strange structure, so called cog-graphs special “molecular networ...

—The graphs which are used in this paper simple, finite and undirected. The first second Zagreb indices for every non-adjacent vertices (also called coindices) dependent only on the degrees interspersed operations of addition multiplication, respectively, vertices. number edges incident vertex v a graph G is degree two u if it’s no common edge between them. In paper, we found coindices chains e...

We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is proportional to its rank raised to the power −α, for some α ∈ (0, 1). Through a rigorous analysis, we show that rank-based attachment models lead to graphs with a p...

the degree of aromaticity of mono-substituted derivatives of benzene has beeninvestigated using a new index based on electric field gradient index, by using two mechanicalquantum methods with gaussian 03. two different basis sets have applied to study and theresults compared. this strategy has demonstrated that, due to violation of symmetry in have pisystems,how the degree of aromaticity can ha...