The path sequence of a graph

Yirong Cai; Hanyuan Deng

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arXiv · 2412.00326

The path sequence of a graph

Yirong Cai·Hanyuan Deng

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Abstract

Let $P(G)=(P_{0}(G),P_{1}(G),\cdots, P_{\rho}(G))$ be the path sequence of a graph $G$, where $P_{i}(G)$ is the number of paths with length $i$ and $\rho$ is the length of a longest path in $G$. In this paper, we first give the path sequences of some graphs and show that the number of paths with length $h$ in a starlike tree is completely determined by its branches of length not more than $h-2$. And then we consider whether the path sequence characterizes a graph from a different point of view and find that any two graphs in some graph families are isomorphic if and only if they have the same path sequence.

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Yirong Cai, Hanyuan Deng. 2024-11-30. The path sequence of a graph. https://arxiv.org/abs/2412.00326

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