Added the picture for paper

Author: joonlee16

content/papers/sparsest_r_robust_graphs.md

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+---
+layout: papers
+# specify the title of the paper
+title:  "Constructing Graphs of Maximum r-Robustness with Minimal Edges"
+# specify the date it was published
+date: 1900-01-01
+# list the authors. if a "/people/id" page exists for the person, it will be linked. If not, the author's name is printed exactly as you typed it. 
+authors:
+    - haejoonl
+    - dimitrapanagou 
+# give the main figure location, relative to /static/
+image: /images/n_r_robust_graphs.png
+# specify the conference or journal that it was published in
+venue: "IEEE CDC 2024"
+# link to publisher site (optional)
+link: 
+# link to arxiv (optional)
+arxiv: 
+# link to github (optional)
+code: 
+# link to video (optional)
+video: 
+# link to pdf (optional)
+pdf: 
+# abstract
+abstract: "In recent years, the notion of r-robustness for the communication graph of the network has been introduced to address the challenge of achieving consensus in the presence of misbehaving agents. Higher r-robustness typically implies higher tolerance to malicious information towards achieving resilient consensus, but it also implies more edges for the communication graph. This in turn conflicts with the need to minimize communication due to limited resources in real-world applications (e.g., multi-robot networks). In this paper, our contributions are twofold. (a) We provide the subgraph structures and tight lower bounds on the number of edges required for graphs with a given number of nodes to reach the maximum robustness. (b) We then use the results of (a) to introduce two classes of graphs that utilize the least number of edges to maintain maximum robustness. Our work is validated through a series of simulations."
+# bib entry (optional). the |- is used to allow for multiline entry.
+bib:
+---