a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

let $gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. denote by $upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. in the classes of graphs $gamma_{n,kappa}$ and $upsilon_{n,beta}$, the elements having maximum augmented zagreb index are determined.

A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.

Abstract An e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V E There are four versions of the problem and the approximation guarantees are as followsAn e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V ...

An efficient heuristic is presented for the problem of finding a minimum-size kconnected spanning subgraph of an (undirected or directed) simple graph G = (V,E). There are four versions of the problem, and the approximation guarantees are as follows: • minimum-size k-node connected spanning subgraph of an undirected graph 1 + [1/k], • minimum-size k-node connected spanning subgraph of a directe...

For Cartesian products G = G1. .. Gm (m 2) of nontrivial connected graphs Gi and the n-dimensional base B de Bruijn graph D = DB(n), we investigate whether or not there exists a spanning subgraph of D which is isomorphic to G. We show that G is never a spanning subgraph of D when n is greater than three or when n equals three and m is greater than two. For n = 3 and m = 2, we can show for wide ...

(m 2) of nontrivial connected graphs G i and the n-dimensional base B de Bruijn graph D = D B (n), we investigate whether or not there exists a spanning subgraph of D which is isomorphic to G. We show that G is never a spanning subgraph of D when n is greater than three or when n equals three and m is greater than two. For n = 3 and m = 2, we can show for wide classes of graphs that G cannot be...