With labeled edges

If the vertices are labelled with labels 1,2,. .., p then there are N = p p - 1) pairs of vertices, all distinct, and the problem of finding the number of such graphs with q edges is simply that of choosing q elements from a set of N elements. This number is, of course, (q). If the vertices are unlabelled, however, the problem is less easy and calls for the use of Polya s Theorem. 

Fig. 20. Schematic representation of the unrolled major groove of the MPD 7 helix showing the first hydration shell, consisting of all solvent molecules that are directly associated with base edge N and O atoms. Base atoms are labeled N4,04, N6,06 and N7 solvent peaks are numbered. Interatomic distances are given in Aup to 3,5 A represented by unbroken lines, between 3,5-4,1 A by dotted lines. The eight circles connected by double-lines represent the image of a spermine molecule bound to phosphate groups P2 and P22. There are 20 solvent molecules in a first hydration layer associated with N- and O-atoms l58)...

The pentagonal dodecahedron (12-sided cavity) of Figure 2.5 is labeled 512 because it has 12 pentagonal faces ( i = 5, nti = 12) with equal edge lengths and... 

Annihilate a graph Suppose we consider a certain graph G with N vertices each of which is denoted by the letter Ki, with the index i labelling the vertices. Now let us delete one of the vertices together with the edges incident at it. This way we get a new graph that has one vertex less ... 

B. Taping with labeling or masking tape Use 3/4 inch wide tape and extend the tape over the sides and bottom edge of the bed. Fold the extended edges of the tape back onto the sides and bottom. Press the contact points firmly to form a good seal. 

Except for the BigH22 structure, the pertinent waves were formulated and plotted. The irreducible representation for which each wave is a basis was determined and labeled in the conventional manner as a species. The corresponding energies were obtained, with each edge being 1.70 A and with the parameter C being (a) 0 and (b) 1.77 A . The results appear in Tables... 

Label (liquid out of two test tubes with corrosion of a metal plate and a hand) upper part black on white background lower part black with white edge... 

Adamantane, C10H15, has the structure shown below. This molecule has Tj symmetry and two types of carbon atoms. There are four methine carbons (each of which is bonded to one hydrogen with label a, h, k, or n) which occupy the corners of a tetrahedron. In addition, there are six methylene carbons (each of which is bonded to two hydrogens) which are located above the edges of the aforementioned tetrahedron. AU 16 hydrogens are labeled in the figure. 

Fig. 3. Mass spectra of photoionized QgCa (top) and C7oCa) (bottom) the lower axis is labeled by the number of metal atoms on the fullerene molecule. The peaks at x = 32 for C Ca and x = 37 for C7oCa , correspond to a first metal layer around the fullerenes with one atom located at each of the rings. The edges at x = 104 and x = 114, respectively, signal the completion of a second metal layer.

A graph G N, M) is labeled if all of its N vertices are associated with N distinct labels in a one-to-one manner. An edge-labeled graph is defined in an analogous fashion. 

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