The semicircle law for semiregular bipartite graphs
نویسندگان
چکیده
We give the (Ahumada type) Selberg trace formula for a semiregular bipartite graph G: Furthermore, we discuss the distribution on arguments of poles of zeta functions of semiregular bipartite graphs. As an application, we present two analogs of the semicircle law for the distribution of eigenvalues of specified regular subgraphs of semiregular bipartite graphs. r 2003 Elsevier Science (USA). All rights reserved.
منابع مشابه
Some Results On Q-Integral Graphs
We consider the problem of determining the Q–integral graphs, i.e. the graphs with integral signless Laplacian spectrum. First, we determine some infinite series of such graphs having the other two spectra (the usual one and the Laplacian) integral. We also completely determine all (2, s)–semiregular bipartite graphs with integral signless Laplacian spectrum. Finally, we give some results conce...
متن کاملZeta functions and complexities of a semiregular bipartite graph and its line graph
We treat zeta functions and complexities of semiregular bipartite graphs. Furthermore, we give formulas for zeta function and the complexity of a line graph of a semiregular bipartite graph. As a corollary, we present the complexity of a line graph of a complete bipartite graph. © 2006 Elsevier B.V. All rights reserved.
متن کاملHall Conditions for Edge-weighted Bipartite Graphs
A weighted variant of Hall’s condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. ...
متن کاملSpectra of random graphs with given expected degrees.
In the study of the spectra of power-law graphs, there are basically two competing approaches. One is to prove analogues of Wigner's semicircle law, whereas the other predicts that the eigenvalues follow a power-law distribution. Although the semicircle law and the power law have nothing in common, we will show that both approaches are essentially correct if one considers the appropriate matric...
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 101 شماره
صفحات -
تاریخ انتشار 2003