2019/01/02 by Tayo Charles Adefokun, Adefokun, Tayo Charles, Deborah Olayide Ajayi +1
Mathematics · #05C15 #05C78 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C15 #msc:05C78
paper · pdf · doi:10.48550/arxiv.1901.00355
9 pages, 2 figures
arxiv created 2019/01/02 · arxiv updated 2019/01/03
A Stacked-book graph Gm,n results from the Cartesian product of a star graph Sm and path Pn, where m and n are the orders of Sm and Pn respectively. A radio labeling problem of a simple and connected graph, G, involves a non-negative integer function f:V(G)→ \mathbb Z+ on the vertex set V(G) of G, such that for all u,v ∈ V(G), |f(u)-f(v)| ≥ \textmddiam(G)+1-d(u,v), where \textmd diam(G) is the diameter of G and d(u,v) is the shortest distance between u and v. Suppose that fmin and fmax are the respective least and largest values of f on V(G), then, spanf, the absolute difference of fmin and fmax, is the span of f while the radio number rn(G) of G is the least value of spanf over all the possible radio labels on V(G). In this paper, we obtain the radio number for the stacked-book graph Gm,n where m ≥ 4 and n is even, and obtain bounds for m=3 which improves existing upper and lower bounds for Gm,n where m=3.