continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

L; U Lower and upper cluster size bounds k Number of clusters Output: P k Restricted k-way partitioning solution Vars: k 0 Index denoting current partitioning size l + 1 Beginning index of possible new cluster 1. 8i; j with L j ? i + 1 U compute w(C i;j]) using Cluster Costs 2. for k 0 = 2 to k do 3. for j = 1 to n do 4.

The concept of the Gutman index, denoted Gut(G) was introduced for a connected undirected graph G. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (directed graphs by definition), and decribe a recursive formula for the Gutman index Gut(J∗ n+1(1)) in terms of the Gutman index of the underlying Jaco graph, J ∗ n (1), n ∈ N with prime Jaconian vertex vi. W...

The detour d(i, j) between vertices i and j of a graph is the number of edges of the longest path connecting these vertices. The matrix whose (i, j)-entry is the detour between vertices i and j is called the detour matrix. The half sum D of detours between all pairs of vertices (in a connected graph) is the detour index, i.e., D = (1/2) Sigma(j) Sigma(i) d(i, j). In this paper, we computed the ...

Introduction. Xanthone glycosides have unique structures and properties. Many efforts focus on the search for C-glycoside derivatives of mangiferin with higher bioavailability. The application QSAR approach allows optimization novel xanthone desired characteristics. Aim. Using available descriptors chemical structure, physical-chemical properties, biological activity, analyze a sample set known...

the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.