Further results on the radio number for some construction of the path, complete, and complete bipartite graphs

Mari, Jeyaraj (2024) Further results on the radio number for some construction of the path, complete, and complete bipartite graphs Heliyon (IF: 3.6) 10(14) e34434

Abstract

Let G be a connected graph with d i a m ( G ) . Then d ( u , v ) indicates the distance of u and v in G. For any pair of distinct vertices u , v of G, mapping from c : V ( G ) → N such that d G ( u , v ) + | c ( u ) - c ( v ) | ≥ d i a m ( G ) + 1 . The maximum label assigned to any vertex of G under a radio labeling c is known as the span of c. The radio number r n ( G ) of G is defined as the minimum span among all possible radio labelings of G. This paper aims to determine the radio number r n ( c ) for specific constructed families of graphs with diameter 3, such as P 2 2 ( N ( m , n ) ) , K 3 , m ( K n c ) , K 3 , m ( n P 3 ) , K 3 , 3 ( 2 K 1 , n ) , and K 5 ( F 3 n ) .© 2024 The Authors.

Links

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11315197
http://www.ncbi.nlm.nih.gov/pubmed/39130467
http://dx.doi.org/10.1016/j.heliyon.2024.e34434

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