arXiv subjects
Publications and source records attributed to Hyeong-Kwan Ju.
In this paper we obtained several properties that the characteristic polynomials of the unit-primitive matrix satisfy. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In fact, Xin and Zhong([4]) showed it earlier. However, we provide simpler method here.
The aim of this work is to introduce several different volume computation methods of the graph polytope associated with various type of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.
Hibi showed that the polynomial in the numerator of the Ehrhart series of a reflexive polytope is palindromic. We proved that those in the numerator of the Ehrhart series of every graph polytope (defined later) of the bipartite graph is palindromic. From this, one of the conjectures (raised in the A205497 of OEIS \cite{[O]}) follows immediately.
We enumerate the number of 0/1-matrices avoiding 2x2 submatrices satisfying certain conditions. We also provide corresponding exponential generating functions.
We enumerate weighted graphs with a certain upper bound condition. We also compute the generating function of the numbers of these graphs, and prove that it is a rational function. In particular, we show that if the given graph is a bipartite graph, then its generating function is of the form $\frac{p(x)}{(1-x)^{m+1}}$, where $m$ is the number of vertices of the graph and $p(x)$ is a polynomial of degree at most $m$.