#### Title

Burning spiders

#### Document Type

Conference Article

#### Publication Title

Communications in Computer and Information Science

#### Abstract

Graph burning is a graph process modeling the spread of social contagion. Initially all the vertices of a graph G are unburned. At each step an unburned vertex is put on fire and the fire from burned vertices of the previous step spreads to their adjacent unburned vertices. This process continues till all vertices are burned. The burning number b(G) of the graph is the minimum number of steps required to burn all the vertices in the graph. The burning number conjecture by Bonato et al. states that for a connected graph G of order n, its burning number (Formula presented). It is easy to observe that in order to burn a graph it is enough to burn its spanning tree. Hence it suffices to prove that for any tree T of order n, its burning number (Formula presented). A spider S is a tree with one vertex of degree at least 3 and all other vertices with degree at most 2. Here we prove that for any spider S of order n, its burning number (Formula presented).

#### First Page

155

#### Last Page

163

#### DOI

10.1007/978-3-319-74180-2_13

#### Publication Date

1-1-2018

#### Recommended Citation

Das, Sandip; Dev, Subhadeep Ranjan; Sadhukhan, Arpan; Sahoo, Uma Kant; and Sen, Sagnik, "Burning spiders" (2018). *Conference Articles*. 169.

https://digitalcommons.isical.ac.in/conf-articles/169