Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

For n ∈ N and 3 ≤ k ≤ n we compute the exact value of Ek(n), the maximum number of edges of a simple planar graph on n vertices where each vertex bounds an l-gon where l ≥ k. The lower bound of Ek(n) is obtained by explicit construction, and the matching upper bound is obtained by using Integer Programming (IP.) We then use this result to conjecture the maximum number of edges of a non-flowerab...

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...

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...

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...

We describe a sufficient condition for graphs used in a construction of Thomassen (which yields hypohamiltonian graphs) to produce maximally non-hamiltonian (MNH) graphs as well. Then we show that the Coxeter graph fulfils this sufficient condition, and thus applying the Thomassen’s construction to multiple copies of the Coxeter graph yields infinitely many MNH graphs with girth 7. So far, the ...