Spiders can be recognized by counting their legs

TL;DR

This paper demonstrates that spiders, a specific class of graphs distinguished by their 8-legged structure, can be identified solely through their degree sequences, providing a new method for recognizing these graphs.

Contribution

It introduces a novel approach to recognize spider graphs directly from degree sequences and fully characterizes their degree sequences.

Findings

Spiders can be recognized from their degree sequences.

Degree sequences of spiders are fully characterized.

The method simplifies identifying spider graphs in graph theory.

Abstract

Spiders are arthropods that can be distinguished from their closest relatives, the insects, by counting their legs. Spiders have 8, insects just 6. Spider graphs are a very restricted class of graphs that naturally appear in the context of cograph editing. The vertex set of a spider (or its complement) is naturally partitioned into a clique (the body), an independent set (the legs), and a rest (serving as the head). Here we show that spiders can be recognized directly from their degree sequences through the number of their legs (vertices with degree 1). Furthermore, we completely characterize the degree sequences of spiders.