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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 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) = (a 0 , a 1 ,. .. , a k−1), where a i is the number of edges incident with v that are… (More)

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