컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0474 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Combinatorics / Graph Theory / Cryptography / Coding Theory (SS-05) |
| 영문제목 (Title(Eng.)) |
Generator subgraphs of wheels and fans |
| 저자(Author(s)) |
Ma. Theresa Christine C. Valdez1, Dr. Severino V. Gervacio2 De La Salle University Dasmarinas1, De La Salle University Manila2 |
| 초록본문(Abstract) | A subgraph $H$ of a graph $G$ is called a generator subgraph of $G$ if the set $\textit{E}_H(G)=\left\{A\vert A\subseteq \textit{E}(G), \bar {A}\cong H\right\}$ spans $\textit{E}(G)$ where $\textit{E}(G)$ is the edge space of $G$ and $\bar {A}$ is the subgraph of $G$ formed by the edges in $A$. The edge space of $G$ is the power set of the set of all edges of $G$. It is a vector space over the field $Z_{2}$ under vector addition defined by $ A\triangle B = (A\setminus B) \cup (B\setminus A) $ and scalar multiplication defined by $c A=A$, if $c=1$ and $c A=\emptyset $, if $c=0$ for all $A,B \in \textit{E}(G)$. This work identified some generator subgraphs of two special classes of graphs namely, wheels and fans. Specifically, this paper shows that $H=P_3\cup P_2$ and $I=P_k$ are both generator subgraphs of wheels and fans and $L=3P_2$ is a generator subgraph of wheels $W_n$ where $n~\geq~6$. |
| 분류기호 (MSC number(s)) |
05C50 |
| 키워드(Keyword(s)) | graphs and linear algebra (matrices, eigenvalues, etc.) |
| 강연 형태 (Language of Session (Talk)) |
English |