Abstract
In this study, we investigate a new kind of mean labeling of graph. The ladder graph plays an important role in the area of communication networks, coding theory, and transportation engineering. Also, we found interesting new results corresponding to classical mean labeling for some ladder-related graphs and corona of ladder graphs with suitable examples.
Highlights
Introduction and PreliminariesAll through this paper, by a graph, we mean an undirected, simple, and finite graph
Let Pn be a path on n nodes denoted by u1,c, where 1 ≤ c ≤ n, and with n − 1 lines denoted by e1,δ, where 1 ≤ δ ≤ n − 1, where ec is the line joining the vertices u1,c and u1,c+1
Let Pn be a path on n nodes denoted by u1,c, where 1 ≤ c ≤ n and with n − 1 lines denoted by e1,δ, where 1 ≤ δ ≤ n − 1, where ec is the line joining the vertices u1,c and u1,c+1
Summary
Introduction and PreliminariesAll through this paper, by a graph, we mean an undirected, simple, and finite graph. Let Pn be a path on n nodes denoted by u1,c, where 1 ≤ c ≤ n, and with n − 1 lines denoted by e1,δ, where 1 ≤ δ ≤ n − 1, where ec is the line joining the vertices u1,c and u1,c+1. E resulting graph is called the one-sided step graph, and it is denoted by STn. Let P2n be a path on 2n vertices u1,c, where 1 ≤ c ≤ 2n and with 2n − 1 edges e1, e2, . E graph obtained is called the double-sided step graph, and it is denoted by 2ST2n. E slanting ladder SLn is a graph obtained from two paths u1, u2, . A ladder graph Ln is the graph P2 × Pn. e graph G ∘ Sm is obtained from G by attaching m pendant vertices to each vertex of G. e triangular ladder TLn, for n ≥ 2, is a graph obtained from two paths by u1, u2, . . . un and v1, v2, . . . vn by adding the edges ucvc, 1 ≤ c ≤ n and ucvc+1, 1 ≤ c ≤ n − 1. e slanting ladder SLn is a graph obtained from two paths u1, u2, . . . un and v1, v2, . . . vn by joining each vc, with uc+1, 1 ≤ c ≤ n − 1. e graph D∗n having the vertices ac,δ: 1 ≤ c ≤ n, δ 1, 2, 3, 4, and its edge set is ac,1ac+1,1, ac,3ac+1,3: 1 ≤ c ≤ n − 1 ∪ ac,1ac,, ac,2ac,, ac,3ac,, ac,4ac,1: 1 ≤ c ≤ n
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