On path energy of graphs

Saieed Akbari, Amir Hossein Ghodrati, Ivan Gutman, Mohammad Ali Hosseinzadeh, Elena V. Konstantinova

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

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 оригиналаанглийский
Страницы (с-по)465-470
Число страниц6
ЖурналMatch
Том81
Номер выпуска2
СостояниеОпубликовано - 1 янв 2019

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  • Цитировать

    Akbari, S., Ghodrati, A. H., Gutman, I., Hosseinzadeh, M. A., & Konstantinova, E. V. (2019). On path energy of graphs. Match, 81(2), 465-470.