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pro vyhledávání: '"DAS, SANDIP"'
We initiate the study of multipacking problems for geometric point sets with respect to their Euclidean distances. We consider a set of $n$ points $P$ and define $N_s[v]$ as the subset of $P$ that includes the $s$ nearest points of $v \in P$ and the
Externí odkaz:
http://arxiv.org/abs/2411.12351
Autor:
Das, Sandip, Gahlawat, Harmender
Cops and Robber is a well-studied two-player pursuit-evasion game played on a graph, where a group of cops tries to capture the robber. The \emph{cop number} of a graph is the minimum number of cops required to capture the robber. Gaven\v{c}iak et al
Externí odkaz:
http://arxiv.org/abs/2408.11002
Given a set $P$ of $n$ points in the plane, in general position, denote by $N_\Delta(P)$ the number of empty triangles with vertices in $P$. In this paper we investigate by how much $N_\Delta(P)$ changes if a point $x$ is removed from $P$. By constru
Externí odkaz:
http://arxiv.org/abs/2402.07775
For a graph $ G = (V, E) $ with a vertex set $ V $ and an edge set $ E $, a function $ f : V \rightarrow \{0, 1, 2, . . . , diam(G)\} $ is called a \emph{broadcast} on $ G $. For each vertex $ u \in V $, if there exists a vertex $ v $ in $ G $ (possi
Externí odkaz:
http://arxiv.org/abs/2312.10485
Autor:
Das, Sandip, Islam, Sk Samim
For a graph $G$, $ mp(G) $ is the multipacking number, and $\gamma_b(G)$ is the broadcast domination number. It is known that $mp(G)\leq \gamma_b(G)$ and $\gamma_b(G)\leq 2mp(G)+3$ for any graph $G$, and it was shown that $\gamma_b(G)-mp(G)$ can be a
Externí odkaz:
http://arxiv.org/abs/2308.04882
Graph burning is a graph process that models the spread of social contagion. Initially, all the vertices of a graph $G$ are unburnt. At each step, an unburnt vertex is put on fire and the fire from burnt vertices of the previous step spreads to their
Externí odkaz:
http://arxiv.org/abs/2308.02825
Autor:
Das, Sandip, Pramanik, Subhamay, Mukherjee, Sumit, Ghosh, Tatan, Nath, Rajib, Kuiri, Probodh K.
Graphene oxide (GO) is one of the important functional materials. Large-scale synthesis of it is very challenging. Following a simple cost-effective route, large-scale GO was produced by mechanical (ball) milling, in air, of carbon nanoparticles (CNP
Externí odkaz:
http://arxiv.org/abs/2307.09011
An $(n,m)$-graph is characterised by having $n$ types of arcs and $m$ types of edges. A homomorphism of an $(n,m)$-graph $G$ to an $(n,m)$-graph $H$, is a vertex mapping that preserves adjacency, direction, and type. The $(n,m)$-chromatic number of $
Externí odkaz:
http://arxiv.org/abs/2306.08069
An oriented graph has weak diameter at most $d$ if every non-adjacent pair of vertices are connected by a directed $d$-path. The function $f_d(n)$ denotes the minimum number of arcs in an oriented graph on $n$ vertices having weak diameter $d$. Findi
Externí odkaz:
http://arxiv.org/abs/2304.00742
The weighted $k$-center problem in graphs is a classical facility location problem where we place $k$ centers on the graph, which minimize the maximum weighted distance of a vertex to its nearest center. We study this problem when the underlying grap
Externí odkaz:
http://arxiv.org/abs/2303.17204