不含整数2的2-系整数组成的可重集的计数公式

为了更好地研究图的组合性质,就特殊图类的伴随等价图的计数问题做了讨论.通过讨论由2-系整数组成且不含整数2的可重集的色等价图的计数问题得到伴随等价图的计数方法.给出了伴随等价图及其补图的色等价图的个数的计算公式.本文提供了一种图的伴随等价计数的新方法,此方法比传统方法更为简洁.     

构造色等价图的几种新方法

给出了构造伴随等价图的几种新方法，因而也给出了构造色等价图的几种新方法。     

具有色多项式∑n＋2／k[k n＋2—k]（λ）k＋1的图

本文讨论了色项式为∑/k≤n 2(n 2)/k[k n 2-k](λ）k 1的图的结构,给出了具有这种色多项式的全部色等价图。     

ω_(aδ)~ω∪bω_δ形图簇的伴随分解及其补图的色等价性

研究图的伴随分解及其补图的色等价性.采用伴随多项式的性质讨论图的伴随分解式,通过图的伴随分解式确定其补图的色性.证明了形图簇的伴随多项式的分解定理,从上述定理得到了这类图簇的补图的色等价性.结论通过图的伴随分解研究其补图的色等价性,是有效的途径与方法,从图的伴随分解式容易看出其补图的色等价图的结构规律.     

几类图簇的伴随多项式的因式分解及色性分析

我们通过研究图的伴随多项式的因式分解，给出了证明非色唯一图的一种新方法，并得到了几类图簇的色等价图的结构特征．     

S~s一类图簇的伴随多项式的因式分解及色性分析

通过研究图的伴随多项式的因式分解 ,给出了证明非色唯一图的一种新方法 ,并且得到了色等价图的一些结构特性 .     

若干图簇的伴随多项式的因式分解及色性分析

我们通过研究图的伴随多项式的因式分解,给出了证明非色唯一图的一种新方法,同时得到若干图簇的色等价图的结构定理.     

S~(GS*)类图簇的伴随多项式的因式分解及其色性

通过研究SGS*类图簇的伴随多项式的因式分解,证明了这类图簇的补图的色等价图的结构特征.     

具有色多项式的图

本文讨论了色多项式为的图的结构,给出了具有这种色多项式的全部色等价图.     

Φ~S-型图簇的伴随分解及其色性分析

运用图的伴随多项式的性质,讨论了图簇ΦS((kn+1)σ,nσ)∪2kSσ的伴随多项式的因式分解定理,进而证明了它们的补图的色等价性.     

Independence equivalence classes of paths

The independence equivalence class of a graph G is the set of graphs that have the same independence polynomial as G. A graph whose independence equivalence class contains only itself, up to isomorphism, is independence unique. Beaton, Brown and Cameron [2] showed that paths with an odd number of vertices are independence unique and raised the problem of finding the independence equivalence class of paths with an even number of vertices. The problem is completely solved in this paper.     

图匹配多项式的因式分解及其应用

通过讨论几类图簇匹配多项式的因式分解,给出了两类图簇匹配等价图的结构性质,从而得到几类新的非匹配唯一图.     

Independence equivalence classes of cycles

The independence equivalence class of a graph G is the set of graphs that have the same independence polynomial as G. Beaton, Brown and Cameron (2019) found the independence equivalence classes of even cycles, and raised the problem of finding the independence equivalence class of odd cycles. The problem is completely solved in this paper.     

完全解决图$\overline{B_{n-8,1,4}}$的色等价类

Two graphs are defined to be adjointly equivalent if and only if their complements are chromatically equivalent.Using the properties of the adjoint polynomials and the fourth character R₄（G）,the adjoint equivalence class of graph B_n-8,1,4 is determined.According to the relations between adjoint polynomial and chromatic polynomial,we also simultaneously determine the chromatic equivalence class of B_n-8,1,4 that is the complement of B_n-8,1,4.     

Graphs realised by r.e. equivalence relations

We investigate dependence of recursively enumerable graphs on the equality relation given by a specific r.e. equivalence relation on ω. In particular we compare r.e. equivalence relations in terms of graphs they permit to represent. This defines partially ordered sets that depend on classes of graphs under consideration. We investigate some algebraic properties of these partially ordered sets. For instance, we show that some of these partial ordered sets possess atoms, minimal and maximal elements. We also fully describe the isomorphism types of some of these partial orders.     

匹配最大根小于等于2的图的匹配等价

给出了十六个匹配等价桥,证明了两个匹配最大根小于等于2的图匹配等价当且仅当它们之间可以由这十六个匹配等价桥进行等价转换,完整地刻画了这些图的补图的匹配等价图类,找到了这些图和它们的补图中的所有匹配唯一图．     

Y(2,2,λ)形图的伴随多项式的分解及其补图的色等价性

构造了两类图簇Y(2,2,λ)∪K1(m为奇数)和Y(2,2,λ)∪EGδ(m为偶数).运用图的伴随多项式,讨论了这两类图簇的伴随多项式的因式分解式,(m=2k-1q-1,λk=(2kq-1)+2k-1qδ),研究了图簇Y(2,2,λk)∪(k-1)K1和Y(2,2,λk)的伴随多项式的因式分解式,进而证明了这些图的补图的色等价性.