• Title/Summary/Keyword: butterfly graph

Search Result 4, Processing Time 0.021 seconds

ON PAIR MEAN CORDIAL GRAPHS

  • R. PONRAJ;S. PRABHU
    • Journal of Applied and Pure Mathematics
    • /
    • v.5 no.3_4
    • /
    • pp.237-253
    • /
    • 2023
  • Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

4-TOTAL DIFFERENCE CORDIAL LABELING OF SOME SPECIAL GRAPHS

  • PONRAJ, R.;PHILIP, S. YESU DOSS;KALA, R.
    • Journal of Applied and Pure Mathematics
    • /
    • v.4 no.1_2
    • /
    • pp.51-61
    • /
    • 2022
  • Let G be a graph. Let f : V (G) → {0, 1, 2, …, k-1} be a map where k ∈ ℕ and k > 1. For each edge uv, assign the label |f(u) - f(v)|. f is called k-total difference cordial labeling of G if |tdf (i) - tdf (j) | ≤ 1, i, j ∈ {0, 1, 2, …, k - 1} where tdf (x) denotes the total number of vertices and the edges labeled with x. A graph with admits a k-total difference cordial labeling is called k-total difference cordial graphs. In this paper we investigate the 4-total difference cordial labeling behaviour of shell butterfly graph, Lilly graph, Shackle graphs etc..

A study on the Digital diorama AR using Natural history Contents (자연사 콘텐츠를 활용한 디지털디오라마 AR연구)

  • Park, Ki-Deok;Chung, Jean-Hun
    • Journal of Digital Convergence
    • /
    • v.19 no.6
    • /
    • pp.293-297
    • /
    • 2021
  • This paper applies the natural history contents of the Science Museum and combines the Gestalt theory to develop the butterfly arrangement structure of the butterfly sample box and the butterfly sample information necessary for the sample box as AR (Augmented Reality). Existing analog sample information is expressed as digital information by combining place, butterfly information, and graph to maximize the effect of digital diorama exhibition. Digital natural history information is increased or decreased, and an environment optimized for real samples and suitability is constructed, and natural history contents are arranged in the principles of collectiveness, closure, simplicity, and continuity using the Gestalt visual perception principle to increase attention and increase the attention of butterfly collection information. Was applied as an application plan of AR.