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pro vyhledávání: '"S., Aparna Lakshmanan"'
All four invariants of the mutual-visibility problem and, all four invariants of the general position problem are determined for glued binary trees. The number of the corresponding extremal sets is obtained in each of the eight situations. The result
Externí odkaz:
http://arxiv.org/abs/2410.17611
Let $G = (V,E)$ be a graph of order $n$ with chromatic number $\chi(G) = k$, let $S \subset V$ and let $C_0$ be a $k$-coloring of the induced subgraph $G[S]$. The coloring $C_0$ is called an extendable coloring, if $C_0$ can be extended to a $k$-colo
Externí odkaz:
http://arxiv.org/abs/2402.08933
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a
Externí odkaz:
http://arxiv.org/abs/2303.00546
Autor:
Varghese, Seena1 graceseenaprince@gmail.com, S., Aparna Lakshmanan2 aparnals@cusat.ac.in, Arumugam, S.3 s.arumugam.klu@gmail.com
Publikováno v:
Communications in Combinatorics & Optimization. 2024, Vol. 9 Issue 2, p205-215. 11p.
The graph $G$ is said to be strongly regular with parameters $(n,k,\lambda,\mu)$ if the following conditions hold: (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have $\lambda$ common neighbours; (3) any two non-adjacent ver
Externí odkaz:
http://arxiv.org/abs/2110.02101
In this paper, we show that if G is strongly regular then the Gallai graph and the anti-Gallai graph of G are edge-regular. We also identify conditions under which the Gallai and anti-Gallai graphs are themselves strongly regular, as well as conditio
Externí odkaz:
http://arxiv.org/abs/2106.03745
Autor:
Varghese, Jismy, S, Aparna Lakshmanan
An Italian dominating function (IDF), of a graph G is a function $ f: V(G) \rightarrow \{0,1,2\} $ satisfying the condition that for every $ v\in V(G) $ with $ f(v) = 0, \sum_{ u\in N(v)} f(u) \geq 2. $ The weight of an IDF on $G$ is the sum $ f(V)=
Externí odkaz:
http://arxiv.org/abs/2009.09989
An Italian dominating function (IDF) of a graph G is a function $ f: V(G) \rightarrow \{0,1,2\} $ satisfying the condition that for every $ v\in V $ with $ f(v) = 0$, $\sum_{ u\in N(v)} f(u) \geq 2. $ The weight of an IDF on $G$ is the sum $ f(V)= \s
Externí odkaz:
http://arxiv.org/abs/2009.09202
Autor:
Varghese, Jismi, S, Aparna Lakshmanan
In this paper, an upper bound for the perfect Italian domination number of the cartesian product of any two graphs is obtained and the exact value of this parameter for cartesian product of some special graphs are obtained. We have also proved that f
Externí odkaz:
http://arxiv.org/abs/1910.12260
Autor:
V., Anu, S., Aparna Lakshmanan
Given a graph $G=(V,E)$, a function $f:V\rightarrow \{0,1,2,3\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\in N(v)$ such that $f(v_{1})=f(v_{2})=2$ or there exists $ w \in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then the
Externí odkaz:
http://arxiv.org/abs/1908.06859