let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.

Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...

A topological index can be focused on uprising of a chemical structure into real number. The degree-based indices have an active place among all indices. These descriptors intentionally associate certain physicochemical assets the corresponding compounds. Graph theory plays very useful role in such type research directions. hex-derived networks vast applications computer science, physical scien...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...