论文标题
图中的顶点多项式及其在图形操作下的行为
Degree polynomial of vertices in a graph and its behavior under graph operations
论文作者
论文摘要
在本文中，我们引入了一个新概念，即用于简单图的顶点的多项式。这个概念导致了一个概念，即多项式序列，比度序列的概念强。在获得一些众所周知的图的多项式序列后，我们证明了一个定理，该定理为在正整数中具有系数的一系列多项式序列提供了必要条件。此外，我们还计算了两个简单图的连接，笛卡尔产品，张量产品和词典产物的多项式，以及简单图的补充的顶点。也给出了一些例子，反例和有关该主题的开放问题
In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for realizability of a sequence of polynomials with coefficients in positive integers. Also we calculate the degree polynomial for vertises of join, Cartesian product, tensor product, and lexicographic product of two simple graphs and for vertices of the complement of a simple graph. Some examples, counterexamples, and open problems concerning to this subjects, is given as well
