the edge versions of reverse wiener indices were introduced by mahmiani et al. veryrecently. in this paper, we find their relation with ordinary (vertex) wiener index in somegraphs. also, we compute them for trees and tuc4c8(s) naotubes.

We establish sharp bounds on the sum and product of the independent domination numbers of a graph and its complement.

Let G be a self-complementary graph (w.) and ir its degree sbquence. Th ;n G has a 2-factor if and only if R 2 is graphic. This is achieved by ohtaming a structure theorem regarding S.C. graphs without a Z-factor. Another irrreresting corollary of the structure theorem is that if G is a s c. graph of order p 3 N with minimum degree at least p/4, then G has a ?-factor and the result is the best ...

In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in G (i.e. the complement graph of G). We apply this correspondence to polynomially solve the cluster deletion problem in a subclass of P4-sparse graphs that strictly includes P4-reducible graphs.

There have been several efforts in the literature to extract as much information as possible from the financial networks. Most of the research has been concerned about the hierarchical structures, clustering, topology and also the behavior of the market network; but not a notable work on the network filtration exists. This paper proposes a stock market filtering model using the correlation - ba...

A graph G is said to be K2,3-saturated if G contains no copy of K2,3 as a subgraph, but for any edge e in the complement of G the graph G + e does contain a copy of K2,3. The minimum number of edges of a K2,2-saturated graph of given order n was precisely determined by Ollmann [6]. Here, we determine the asymptotic behavior for the minimum number of edges in a K2,3-saturated graph.

The question of whether the characteristic polynomial of a simple graph is uniquely determined by the characteristic polynomials of its vertex-deleted subgraphs is one of the many unresolved problems in graph reconstruction. In this paper we prove that the characteristic polynomial of a graph is reconstructible from the characteristic polynomials of the vertex-deleted subgraphs of the graph and...

For a class $$\mathcal {G}$$ of graphs, the problem Subgraph Complement to asks whether one can find subset S vertices input graph G such that complementing subgraph induced by in results . We investigate complexity when is H-free for H being complete graph, star, path, or cycle. obtain following results: Further, we prove these hard problems do not admit subexponential-time algorithms (algorit...