No abstract

Graph labeling plays an important role in different branches of sciences. It gives useable information in the study of radar, missile and rocket theory. In scheme theory, coding theory and computer networking graph labeling is widely employed. In the present paper, we find necessary conditions for the octagonal planner map and multiple wheel graph to be super cyclic antimagic cover and then discuss their super cyclic antimagic covering.

In this article, we study the approximate fixed point sequence of an evolution family. A family E � U(x, y); x ≥ y ≥ 0 of a bounded nonlinear operator acting on a metric space (M, d) is said to be an evolution family if U(x, x) � I and U(x, y)U(y, z) � U(x, z) for all x ≥ y ≥ z ≥ 0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.

In this paper we deal with the problem of labeling the vertices, edges, and faces of a toroidal fullerene H n m with mn hexagons by the consecutive integers from 1 up to |V (H n m| in such a way that the set of face-weights of 6 -sided faces forms an arithmetic progression with common difference d , where by face-weight we mean the sum of the label of that face and the labels of vertices and edges surrounding that face.The paper examines the existence of such labelings for several differences d .

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.