Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

Abstract The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees (tree that visiting all the vertices of the graph G). Let Cn be a cycle with n vertices. The Star flower planar map is a simple graph G formed from a cycle Cn by adding a vertex adjacent to every edge of Cn and we connect this vertex with two end vertices of each edge of Cn,...

We propose a methodology for representing artificial creatures like 3D flowers. Directed graph and Lindenmayer system (L-system) are commonly involved in AI-based creativity research for encoding ceatures. It is difficult for L-systems to directly feed back real morphologies structurally from their genotypes, since they are a grammatical rewriting system and also use parameters such as loops, p...

If each subgraph of the decomposition π graph G has Steiner number same as then is said to be a G. The maximum cardinality among and denoted by πst(G). In this paper, we present for Complete n-Sun graph.

Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wh...

Deciding whether an arbitrary graph contains a sun was recently shown to be NP-complete [10]. We show that whether a building-free graph contains a sun can be decided in O(min{mn,mn}) time and, if a sun exists, it can be found in the same time bound. The class of building-free graphs contains many interesting classes of perfect graphs such as Meyniel graphs which, in turn, contains classes such...

In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which ha...

We describe an algorithm for automatically segmenting flowers in colour photographs. This is a challenging problem because of the sheer variety of flower classes, the intra-class variability, the variation within a particular flower, and the variability of imaging conditions – lighting, pose, foreshortening etc. The method couples two models – a colour model for foreground and background, and a...