| Title | : | On Distance Magic Graphs: Characterization Challenges |
| Speaker | : | Ravindra Kuber Pawar (BITS Goa) |
| Details | : | Wed, 25 Sep, 2024 2:30 PM @ SSB 334 |
| Abstract: | : | Abstract: A simple, finite graph G is said to be distance magic if its vertices can be labeled in one-to-one manner using the numbers 1, 2, . . . , |V (G)| such that the sum of the labels in the open neighborhood of any given vertex is the same. This constant sum is called the magic constant of the graph. This definition raises two questions: which natural numbers can be magic constants? and which graphs are distance magic? It is believed that among all graphs on the given number of vertices only a fraction of them are distance magic. For example, among all simple graphs of order up to 10, there are only 23 such graphs. Furthermore, a forbidden subgraph characterization for this class of graphs is not possible, making it difficult to characterize them. In this talk, we will address both of the above questions. We will present an algorithm to generate such graphs of a given order with given magic constant. Additionally, we will discuss the current status of the computational complexity involved in determining whether a given graph G is distance magic. Furthermore, we will explore some spectral properties of these graphs and discuss results that relate the distance magic property to the graph’s spectrum. This work is in collaboration with Himadri Mukherjee (BITS Goa), Jay Bagga (BSU, USA) and Tarkeshwar Singh (BITS Goa). |
