Aparna S. Lakshmanan

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7 papers · 1 filter

math.CO2025

Mutual-visibility Coloring of Graphs

Saneesh Babu, Gabriele Di Stefano, Aparna Lakshmanan S

The mutual-visibility chromatic number of a graph $G$ is the smallest number of colors needed to color the vertices of $G$ such that each color class is a mutual-visibility set. In…

math.CO2025

Ramsey sequences with bounded clique size

Abhishek Girish Aher, Aparna Lakshmanan S

A sequence of graphs ${G_{k}}$ is a Ramsey sequence if for every positive integer $k$ , the graph $G_{k}$ is a proper subgraph of $G_{k + 1}$ , and there exists an integer $n > k…

math.CO2025

Varieties of mutual-visibility and general position on Sierpiński graphs

Dhanya Roy, Sandi Klavžar, Aparna Lakshmanan +1

The variety of mutual-visibility problems contains four members, as does the variety of general position problems. The basic problem is to determine the cardinality of the largest…

math.CO2025

Erdős Conjecture and AR-Labeling

Arun J Manattu, Aparna Lakshmanan S

Given an edge labeling $f$ of a graph $G$ , a vertex $v$ is called an $A R$ -vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$ . An injecti…

math.CO2025

On Geodesic Leech Labeling of Some Graph Classes

Aparna Lakshmanan S, Arun J Manattu

Let $f : E \to {1, 2, 3, \dots}$ be an edge labeling of $G$ . The geodesic path number of $G$ , $t_{g p} (G)$ , is the number of geodesic paths in $G$ . An edge labeling $f$ is calle…

math.CO2025

An edge labeling of graphs from Rados partition regularity condition

Arun J Manattu, Aparna Lakshmanan S

A vertex $v$ is called an AR-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$ . i.e., if ${x_{1}, x_{2}, \dots, x_{k}}$ are the edge labels of…

math.CO2019

On the Double Roman Domination Number of Generalized Sierpinski Graphs

Anu V., Aparna Lakshmanan S.

In this paper, we study the double Roman domination number of generalized Sierpiński graphs $S (G, t)$ . More precisely, we obtain a bound for the double Roman domination number of $S…