Article Per Year (5 Year)
p-Index From 2020 - 2025
0
P-Index
This Author published in this journals
All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Henry Escuadro
Department of Mathematics, Juniata College, Huntingdon, PA, USA
Electrical & Electronics Engineering

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
A graph theoretical analysis of the number of edges in k-dense graphs Linda Eroh; Henry Escuadro; Ralucca Gera; Samuel Prahlow; Karl Schmitt
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.1.4

Abstract

Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or subgraph) detection within a network/graph, we focused on finding characterizations of k-dense communities. For each edge $uv\in E(G)$, the {\bf edge multiplicity} of $uv$ in $G$ is given by $m_G(uv)=|N_{G}(u)\cap N_{G}(v)|.$ For an integer $k$ with $k\ge 2$, a {\bf $\boldsymbol{k}$-dense community} of a graph $G$, denoted by $DC_k(G)$, is a maximal connected subgraph of $G$ induced by the vertex set$V_{DC_k(G)} = \{v\in V(G) : \exists u\in V(G)\ {\rm such\ that\ } uv\in E(G)\ {\rm and\ } m_{DC_{k(G)}}(uv)\ge k-2\}.$In this research, we characterize which graphs are $k$-dense but not $(k+1)$-dense for some values of $k$ and study the minimum and maximum number of edges such graphs can have. A better understanding of $k$-dense sub-graphs (or communities) helps in the study of the connectivity of large complex graphs (or networks) in the real world.
Co-Authors Karl Schmitt Linda Eroh Ralucca Gera Samuel Prahlow