Subgraphs Maximal

Strong operator convergence, 616 Sturm sequence, 77 Subgraph, 256 maximal connected, 256 Subgroup decomposition of point groups, 738... 

McGregor, J. and Willett, P. (1981) Use of a maximal common subgraph algorithm in the automatic identification of the ostensible bond changes occurring in chemical reactions../. Chem. Inf. Comput. Sci. 21, 137-140. 

Two vertices are called adjacent if they share a common edge. A path is a sequence of adjacent vertices. A graph is connected if any two of its vertices are linked by a path. A maximal connected subgraph of graph G is called a connected component of G. Every graph can be decomposed into connected components. 

Now we consider another natural notion of maximality for polycycles. An (r, q)-polycycle is called rum-extensible if it is not a partial subgraph of any other (r, extensible polycycles are helicenes. It is also clear that any 3-connected (r, 3)-polycycle is non-extensible. 

Barrow, H. G. and R. M. Burstall, "Subgraph Isomorphism, Matching Relational Structures, and Maximal Cliques," Information Processing Letters, (4), 83-84 (January 1976). 

The components (maximal connected subgraphs) of these diagrams are termed islands. The number of little islands with 2-sites in a superposition diagram S is denoted by i(S), and the number of larger big islands is denoted by I(S). Then Pauling showed that... 

Therefore, searching for some edge-weighted maximal common subgraph for the two complete graphs is equivalent to searching for a clique [58] in this... 

Given two graphs Gi and G2, if there exists a subgraph of order k of Gi isomorphic to a subgraph 5 of G2, the pair of isomorphic subgraphs S, S ) is called a common subgraph of order k of Gi and G2. A common subgraph is maximal if there is no common... 

H.G. Barrow, R.M. Burstall, Subgraph Isomorphism, Matching Relational Structures and Maximal Cliques, Information Proc-cesing Letters, 4 (1976) 83-84. 

A maximal complete subgraph in which every vertex is connected to every other vertex and which is not contained in any other larger subgraph with this property. 

For convenience, in the subsequent sections of this chapter, the mathematical terms introduced above, such as graph, subgraph, and maximal common subgraph, are interchangeably used with the corresponding chemical terms, such as structure, substructure, and maximal common substructure. 

A complete subgraph of a graph is also called a clique. A clique is maximal if it is not contained in any other clique [62]. A maximum clique is the maximal clique with... 

---