Аннотация
For a graph G with vertex set {v1, . . ., v n }, let P(G) be an n × n matrix whose (i, j)-entry is the maximum number of internally disjoint viv j -paths in G, if i ≠ j, and zero otherwise. The sum of absolute values of the eigenvalues of P(G) is called the path energy of G, denoted by PE. We prove that PE of a connected graph G of order n is at least 2(n− 1) and equality holds if and only if G is a tree. Also, we determine PE of a unicyclic graph of order n and girth k, showing that for every n, PE is an increasing function of k. Therefore, among unicyclic graphs of order n, the maximum and minimum PE-values are for k = n and k = 3, respectively. These results give affirmative answers to some conjectures proposed in MATCH.
Язык оригинала | английский |
---|---|
Страницы (с-по) | 465-470 |
Число страниц | 6 |
Журнал | Match |
Том | 81 |
Номер выпуска | 2 |
Состояние | Опубликовано - 1 янв 2019 |
Предметные области OECD FOS+WOS
- 1.04 ХИМИЧЕСКИЕ НАУКИ
- 1.02 КОМПЬЮТЕРНЫЕ И ИНФОРМАЦИОННЫЕ НАУКИ
- 1.01 МАТЕМАТИКА