Degree of a vertex

The ring degree of a vertex Vj belonging to a cyde, denoted as p , is a local vertex invariant defined as the minimum number of nonhydrogen vertices bonded to vertex Vj, which must be removed to transform the ith vertex into an acyclic one [Cao and Yuan, 2001]. 

The degree of a vertex with a loop is taken to be the number of edges incident to this vertex plus two for the loop (for instance, a lone pair), because the loop contributes twice to the number of edges incident at that vertex [Lukovits, Milicevic et al, 2002]. 

Hollas, B. (2005b) On the variance of topological indices that depend on the degree of a vertex. MATCH Commun. Math. Comput. Chem., 54, 341-350. 

The degree of a vertex in the topological representation corresponds to the number of distinet permutational isomers that can be generated in a single isomerization from the isomer represented by the vertex in question this number 6 is called the connectivity. For topologjeally distinct polyhedra depicted in the same topological representation, the isomer counts I and I and connectivities 6 and 6 must satisfy the so-called closure condition, i.e. ... 

Definition 1 The degree of a vertex v, kv, is the number of edges incident to v. The mean degree, z, of a graph G is defined as follows ... 

The Randic index (x) is the sum of the p, terms. Let 8 be the degree of a vertex of the graph and then define 5, and Sj as the degrees of two vertices that are connected. The link (edge) between these vertices is characterized by p (the inverse of the geometrical mean of the degrees). The sum of all p values is the index Randic X... 

Although it is not addressed here, the vertex degree of directed graphs/networks can be handled by assessing the in-degree and out-degree of a vertex that corresponds, respectively, to the number of edges directed towards the vertex and the number directed away from the vertex. 

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