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Suppose each edge of a simple connected undirected graph is given a unique number from the numbers 1, 2, . . ., q, where q is the number of edges of that graph. Then each vertex is labelled with sum of the labels of the edges incident to it. If no two vertices have the same label, then the graph is called an antimagic graph. We prove that the Cartesian product of wheel graph and path graph is antimagic. [ABSTRACT FROM AUTHOR]

Let G=(E(G),V(G)) be a (molecular) graph with vertex set V(G) and edge set E(G). The forgotten Zagreb index and the hyper Zagreb index of G are defined by F(G)=∑u∈V(G)d(u)3 and HM(G)=∑uv∈E(G)(d(u)+d(v))2 where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. A recent problem called the inverse problem deals with the numerical realizations of topological indices. We see that there exist trees for all even positive integers with F(G)>88 and with HM(G)>158. Along with the result, we show that there exist no trees with F(G)<90 and HM(G)<160 with some exceptional even positive integers and hence characterize the forgotten Zagreb index and the hyper Zagreb index for trees. [ABSTRACT FROM AUTHOR]

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) is a complete graph. In this paper, we find the line completion number of grid graph Pn Pm for various cases of n and m. [ABSTRACT FROM AUTHOR]

The concept of Lucky k-polynomials and in particular Lucky X-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky X-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind. [ABSTRACT FROM AUTHOR]

The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r-edges of G, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number lc(G) of a graph G is the least positive integer r for which Lr(G) is a complete graph. In this paper, we find the line completion number of grid graph Pn Pm for various cases of n and m. [ABSTRACT FROM AUTHOR]

In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative integers. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. We find the edge coloring number of these grids to be 9, 7 and 16, respectively so that we could color the edges of a rectangular, hexagonal and triangular grid with at most 10, 8 and 17 colors, respectively using this coloring technique. Repeating the sequence pattern for different grids, we can color the edges of a grid of larger size. [ABSTRACT FROM AUTHOR]