M. Mollard

activity

20122022

most citedOn domination of Cartesian product of directed cycles

2 citations · 2 across the 10 of their papers we have counts for

collaborators

12 papers

math.CO2022

A relation between Wiener index and Mostar index for daisy cubes

Michel Mollard

Daisy cubes are a class of isometric subgraphs of the hypercubes Q n. Daisy cubes include some previously well known families of graphs like Fibonacci cubes and Lucas cubes. Moreov…

math.CO2021

Edges in Fibonacci cubes, Lucas cubes and complements

Michel Mollard

The Fibonacci cube of dimension n, denoted as $Γ_n$ , is the subgraph of the hypercube induced by vertices with no consecutive 1's. The irregularity of a graph G is the sum of |d(x…

math.CO2020

The (non-)existence of perfect codes in Lucas cubes

Michel Mollard

The Fibonacci cube of dimension n, denoted as $Γ$ n , is the subgraph of the n-cube 5 Q n induced by vertices with no consecutive 1's. Ashrafi and his co-authors proved the non-exi…

math.CO2018

Perfect codes in generalized Fibonacci cubes

Michel Mollard

The {\em Fibonacci cube} of dimension $n$ , denoted as $Γ_n$ , is the subgraph of the $n$ -cube $Q_n$ induced by vertices with no consecutive 1's. In an article of 2016 Ashrafi and…

math.CO2017

Daisy cubes and distance cube polynomial

Sandi Klavžar, Michel Mollard

Let X $\subseteq$ {0, 1} n. Then the daisy cube Q n (X) is introduced as the sub-graph of Q n induced by the intersection of the intervals I(x, 0 n) over all x $\in$ X. Daisy cubes…

math.CO2016

Non covered vertices in Fibonacci cubes by a maximum set of disjoint hypercubes

Michel Mollard

The Fibonacci cube of dimension n, denoted as $Γ$ n , is the subgraph of n-cube Q n induced by vertices with no consecutive 1's. In this short note we prove that asymptotically all…

math.CO2015

On Disjoint hypercubes in Fibonacci cubes

Sylvain Gravier, Michel Mollard, Simon Spacapan +1

The {\em Fibonacci cube} of dimension $n$ , denoted as $Γ_n$ , is the subgraph of $n$ -cube $Q_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoin…

math.CO2013

Asymptotic Properties of Fibonacci Cubes and Lucas Cube

Sandi Klavzar, Michel Mollard

It is proved that the asymptotic average eccentricity and the asymptotic average degree of Fibonacci cubes and Lucas cubes are $(5 + 5) /10$ and $(5 - 5) /5$ , respectively. A…

math.CO2012★ 2 cited

On domination of Cartesian product of directed cycles

Michel Mollard

Let $γ (C_{m} □ C_{n})$ be the domination number of the Cartesian product of directed cycles $C_{m}$ and $C_{n}$ for $m, n \geq 2$ . Shaheen [] and Liu and al.[ ], [ ] determined the value of…

math.CO2012

Edge Decompositions of Hypercubes by Paths and by Cycles

Michel Mollard, Mark Ramras

If $H$ is (or is isomorphic to) a subgraph of $G$ , $H$ is said to {\it divide} $G$ if there is an edge-decomposition of $G$ by copies of $E (H)$ , the edge set of $H$ . A more restric…

math.CO2012

Maximal hypercubes in Fibonacci and Lucas cubes

Michel Mollard

The Fibonacci cube $Γ_{n}$ is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $Λ_{n}$ is obtained from $Γ_{n}$ by removing…

cs.DM2012

New results on variants of covering codes in Sierpinski graphs

Sylvain Gravier, Matjaz Kovse, Michel Mollard +2

In this paper we study identifying codes, locating-dominating codes, and total-dominating codes in Sierpinski graphs. We compute the minimum size of such codes in Sierpinski graphs…