Super total labeling (a,d)-edge antimagic on the firecracker graph

An An (a, d)-edge antimagic total labeling on (p, q)-graph G is a one-to-one map f from V (G) ∪ E(G) onto the i nteger s 1, 2, . . ., p + q with the property that the edge-weights, w(uv) = f (u) + f(v) + f(uv) where uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Such labeling is cal led super if the smal lest possible labels appear on the vertices. In this paper, we investigate the existence of super (a, d)-edge antimagic total labeling of Firecracker Graph

Ideal bases in constructions defined by directed graphs

The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. Our main theorem establishes that, for every balanced digraph D and each idempotent semiring R with 1, the incidence semiring ID(R) of the digraph D has a convenient visible ideal basis BD(R). It also shows that the elements of BD(R) can always be used to generate two-sided ideals with the largest possible weight among the weights of all two-sided ideals in the incidence semiring

Ideal Basis in Constructions Defined by Directed Graphs

The present article continues the investigation of visible ideal bases in constructions defined using directed graphs. This notion is motivated by its applications for the design of classication systems. Our main theorem establishes that, for every balanced digraph and each idempotent semiring with identity element, the incidence semiring of the digraph has a convenient visible ideal basis. It also shows that the elements of the basis can always be used to generate ideals with the largest possible weight among the weights of all ideals in the incidence semiring

On d-antimagic labelings of plane graphs

The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face.A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices.In the paper we examine the existence of such labelings for several families of plane graphs