We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Square Graphs.
- Authors
Abdullah, Mahmood Madian; Ali, Ahmed Mohammed
- Abstract
In a connected graph 𝐺, the distance function between each pair of two vertices from a set vertex 𝑉(𝐺) is the shortest distance between them and the vertex degree 𝑢 denoted by 𝑑𝑒𝑔𝑢 is the number of edges which are incident to the vertex 𝑢. The Schultz and modified Schultz polynomials of 𝐺 are have defined as: 𝑆𝑐(𝐺; 𝑥) = ∑( 𝑑𝑒𝑔𝑢 + 𝑑𝑒𝑔𝑣) 𝑥 𝑑(𝑢,𝑣) 𝑎𝑛𝑑 𝑆𝑐 ∗ (𝐺; 𝑥) = ∑ (𝑑𝑒𝑔𝑢. 𝑑𝑒𝑔𝑣) 𝑥 𝑑(𝑢,𝑣), respectively, where the summations are taken over all unordered pairs of distinct vertices in 𝑉(𝐺) and 𝑑(𝑢, 𝑣) is the distance between 𝑢 and 𝑣 in 𝑉(𝐺). The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.
- Subjects
POLYNOMIALS; CHARTS, diagrams, etc.; GRAPH connectivity; SQUARE
- Publication
Baghdad Science Journal, 2022, Vol 19, Issue 3, p560
- ISSN
2078-8665
- Publication type
Article
- DOI
10.21123/bsj.2022.19.3.0560