-
3
-
-
0001264199
-
-
C. Domb, M.S. Green (Eds.), Academic Press, New York
-
E.H. Lieb, F.Y. Wu, in: C. Domb, M.S. Green (Eds.), Phase Transitions and Critical Phenomena, vol. 1, Academic Press, New York, 1972, p. 331.
-
(1972)
Phase Transitions and Critical Phenomena
, vol.1
, pp. 331
-
-
Lieb, E.H.1
Wu, F.Y.2
-
8
-
-
9344220161
-
-
note
-
We recall the strict mathematical definition of a graph as a finite collection of vertices and bonds connecting (all or a subset of the) vertices, such that there are (i) no loops, i.e., bonds connecting a vertex to itself and (ii) no multiple bonds connecting a given pair of vertices. We denote the limit as the number of vertices of a family of graphs G goes to infinity as {G}.
-
-
-
-
14
-
-
0002461816
-
Chromatic polynomials
-
E.W. Beineke, R.J. Wilson (Eds.), Academic Press, New York
-
R.C. Read, W.T. Tutte, Chromatic polynomials, in: E.W. Beineke, R.J. Wilson (Eds.), Selected Topics in Graph Theory, vol. 3, Academic Press, New York, 1988.
-
(1988)
Selected Topics in Graph Theory
, vol.3
-
-
Read, R.C.1
Tutte, W.T.2
-
15
-
-
0004105733
-
-
G.G. Rota (Ed.), Addison-Wesley, New York
-
W.T. Tutte, in: G.G. Rota (Ed.), Graph Theory, Encyclopedia of Mathematics and its Applications, vol. 21, Addison-Wesley, New York, 1984.
-
(1984)
Graph Theory, Encyclopedia of Mathematics and Its Applications
, vol.21
-
-
Tutte, W.T.1
-
16
-
-
0003780715
-
-
Addison-Wesley, Reading
-
F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.
-
(1969)
Graph Theory
-
-
Harary, F.1
-
17
-
-
0004242420
-
-
Cambridge, U.K., Cambridge Univ. Press, 1st ed. 1974, 2nd ed.
-
N.E. Biggs, Algebraic Graph Theory, Cambridge, U.K., Cambridge Univ. Press, 1st ed. 1974, 2nd ed. 1993.
-
(1993)
Algebraic Graph Theory
-
-
Biggs, N.E.1
-
30
-
-
9344254062
-
-
note
-
Relevant carlier papers on ℬ are Refs. [31-34]. (The locus ℬ for ladder graphs given in Refs. [31,34] were not quite correct; the correct locus was given in Ref. [19]; see also the comment in Ref. [26].)
-
-
-
-
34
-
-
0001358201
-
-
Wiley, New York
-
R.C. Read, G.F. Royle, Graph Theory, Combinatorics, and Applications, vol. 2, Wiley, New York, 1991, p. 1009.
-
(1991)
Graph Theory, Combinatorics, and Applications
, vol.2
, pp. 1009
-
-
Read, R.C.1
Royle, G.F.2
-
35
-
-
9344231631
-
-
note
-
y = 2 strip of the triangular lattice.
-
-
-
-
40
-
-
9344245947
-
-
note
-
n is thus the graph with n vertices and no bonds.
-
-
-
-
42
-
-
9344237889
-
-
note
-
contr,q).
-
-
-
-
44
-
-
9344231074
-
-
note
-
k,r, the resultant boundary ℬ is given by the compact locus of Eq. (5.3).
-
-
-
-
45
-
-
9344250213
-
-
Ph.D. thesis, State Univ. of New York, April
-
Additional figures giving the respective ℬ and chromatic zeros for higher values of k are given in S.-H. Tsai, Ph.D. thesis, State Univ. of New York, April, 1998.
-
(1998)
-
-
Tsai, S.-H.1
-
46
-
-
9344251878
-
-
note
-
i.
-
-
-
-
53
-
-
9344250772
-
-
American Mathematical Society, Providence, RI
-
V. Kharlamov et al. (Eds.), AMS Translations, vol. 173, American Mathematical Society, Providence, RI, 1996.
-
(1996)
AMS Translations
, vol.173
-
-
Kharlamov, V.1
|