Illya V. Hicks

activity

20122026

most citedGraphs with Extremal Connected Forcing Numbers

2 citations · 2 across the 11 of their papers we have counts for

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5 papers · 1 filter

math.CO2026

Randomized Zero Forcing

Jesse Geneson, Illya Hicks, Noah Lichtenberg +2

We introduce randomized zero forcing (RZF), a stochastic color-change process on directed graphs in which a white vertex turns blue with probability equal to the fraction of its in…

math.CO2020

An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs

Logan A. Smith, David T. Mildebrath, Illya V. Hicks

We present an integer programming model to compute the strong rainbow connection number, $sr c (G)$ , of any simple graph $G$ . We introduce several enhancements to the proposed model,…

math.CO2019

A Polynomial Time Algorithm for Computing the Strong Rainbow Connection Numbers of Odd Cacti

Logan A. Smith, David T. Mildebrath, Illya V. Hicks

We consider the problem of computing the strong rainbow connection number $sr c (G)$ for cactus graphs $G$ in which all cycles have odd length. We present a formula to calculate $src…

math.CO2018

Power domination throttling

Boris Brimkov, Joshua Carlson, Illya V. Hicks +2

A power dominating set of a graph $G = (V, E)$ is a set $S \subset V$ that colors every vertex of $G$ according to the following rules: in the first timestep, every vertex in $N [S]$ be…

math.CO2012

A Note on Integer Domination of Cartesian Product Graphs

K. Choudhary, S. Margulies, I. V. Hicks

Given a graph $G$ , a dominating set $D$ is a set of vertices such that any vertex in $G$ has at least one neighbor (or possibly itself) in $D$ . A $k$ -dominating multiset $D_{k}$ is…