Henry Escuadro

On the hardness of recognizing triangular line graphs

Given a graph G, its triangular line graph is the graph T (G) with vertex set consisting of the edges of G and adjacencies between edges that are incident in G as well as being within a common triangle. Graphs with a representation as the triangular line graph of some graphG are triangular line graphs, which have been studied under many names including anti-Gallai graphs, 2-in-3 graphs, and link graphs. While closely related to line graphs, triangular line graphs have been dicult to understand and characterize. Van Bang Le asked if recognizing triangular line graphs has an ecient algorithm or is computationally complex. We answer this question by proving that the complexity of recognizing triangular line graphs is NP-complete via a reduction from 3-SAT.

A Graph Theoretical Analysis of the Number of Edges in k-Dense Graphs

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

A Note on the Total Detection Numbers of Cycles

uv\in E(G)

Detour distance in graphs

, the {\bf edge multiplicity} of

Detectable colorings of graphs

uv

A three-color problem in graph theory

in

Geodetic Domination in Graphs

G

On detectable colorings of graphs

is given by

Vertex-distinguishing colorings of graphs -- A survey of recent developments

m_G(uv)=|N_{G}(u)\cap N_{G}(v)|.

On detectable factorizations of cubic graphs

For an integer