Henry Escuadro

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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 graph G are triangular line graphs, which have been studied under many names including(More)
Linguists often represent the relationships between words in a collection of text as an undirected graph G = (V,E), were V is the vocabulary and vertices are adjacent in G if and only if the words they represent co-occur in a relevant pattern in the text. Ideally, the words with similar meanings give rise to the vertices of a component of the graph.(More)
Let G be a connected graph of order n ≥ 3 and let c : E(G) → {1, 2, . . . , k} be a coloring of the edges of G (where adjacent edges may be colored the same). For each vertex v of G , the color code of v with respect to c is the k -tuple c(v) = (a1, a2, · · · , ak) , where ai is the number of edges incident with v that are colored i ( 1 ≤ i ≤ k ). The(More)
Let G be a connected graph of size at least 2 and c :E(G)→{0, 1, . . . , k− 1} an edge coloring (or labeling) of G using k labels, where adjacent edges may be assigned the same label. For each vertex v of G, the color code of v with respect to c is the k-vector code(v) = (a0, a1, . . . , ak−1), where ai is the number of edges incident with v that are(More)
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 sub-graph) detection within a network/graph, we focused on finding characterizations of k-dense communities. For each edge uv ∈ E(G), the edge multiplicity(More)
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