Cyclic-antimagic construction of ladders

Abstract

A simple graph G = (V, E) admits an H-covering if every edge in the edge set E(G) belongs to at least one subgraph of G isomorphic to a given graph|} defines a bijective map such that, for all subgraphs H of G isomorphic to H, the sums of labels of all vertices and edges belonging to H constitute an arithmetic progression with the initial term a and the common difference d. Such a graph is named as super (a, d)-H-antimagic if h(V(G)) = {1, 2, 3, . . . , |V(G)|}. For d = 0, the super (a, d)-H-antimagic graph is called H-supermagic. In the present paper, we study the existence of super (a, d)-cycle-antimagic labelings of ladder graphs for certain differences d.

Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules

“…A molecular graph is a simple graph in which atoms and bonds are represented by vertex and edge sets, respectively. e vertex degree is the number of edges attached to that vertex [10][11][12][13][14][15][16]. e maximum degree of vertex among the vertices of a graph is denoted by Δ(G).…”

Irregularity Measures for Metal-Organic Networks

“…Graph theory provides the interesting appliance in mathematical chemistry that is used to compute the various kinds of chemical compounds by means of graph theory and predict their various properties [13][14][15][16][17][18][19]. One of the most important tools in the chemical graph theory is a topological index, which is useful in predicting the chemical and physical properties of the underlying chemical compound, such as boiling point, strain energy, rigidity, heat of evaporation, and tension [20,21].…”

H-Coverings of Path-Amalgamated Ladders and Fans

“…Susanto [7] derived bound for cycle-antimagic labeling of disjoint union of cycles. Recent results on H-antimagic labeling of graphs can be seen in [8][9][10][11][12][13][14]. Also, in [12], Baca et al discussed the tree-antimagicness of disconnected graphs.…”

“…Baca et al proved d-antimagic labeling of type (1, 1, 1) for toroidal fullerenes in [18], while, in [19], Baca et al proved labeling for plane graphs containing Hamiltonian paths. For more details, we refer [20][21][22][23][24][25][26][27][28][29] and the references therein. In the present article, we have studied super H-antimagic labeling of path-amalgamation of ladder and fan for several differences, where H is isomorphic to cycles C 3 , C 4 , C 5 , and P 2 -amalgamation of two cycles C 3 and C 4 .…”