Wiener index of trees of given order and diameter at most 6

The long-standing open problem of finding an upper bound for the Wiener index of a graph in terms of its order and diameter is addressed. Sharp upper bounds are presented for the Wiener index, and the related degree distance and Gutman index, for trees of order $n$ and diameter at most $6$. DOI: 10.1017/S000497271300081

The Ramsey number for two graphs of order 5

For two graphs F1 and F2, the Ramsey number R(F1, F2) is the smallest positive integer r such that for every graph G on r vertices, G contains F1 as a subgraph or the complement of G contains F2 as a subgraph. We present the exact value of the Ramsey number R(?5, W5), where ?5 is the cycle with a chord and W5 is the wheel, both having 5 vertices. � 2018, � 2018 Taru Publications.The work of T. Vetr�k was supported by the National Research Foundation of South Africa; Grant numbers: 112122, 90793.Scopu