Abstract The Gallai graph Γ (G) of a graph G, has the edges of G as its vertices and two
distinct edges are adjacent in Γ (G) if they are incident in G, but do not span a triangle. The …

Abstract The Gallai graph Γ (G) of a graph G, has the edges of G as its vertices and two
distinct vertices are adjacent in Γ (G) if they are adjacent edges in G, but do not lie on a …

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 …

Let G=(V, E) be a graph. The Gallai total graph ΓT (G) of G is the graph, where V (ΓT (G))=
V∪ E and uv∈ E (ΓT (G)) if and only if (i) u and v are adjacent vertices in G, or (ii) u is …

Graph theory is rooted in the eighteenth century, beginning with the work of Euler, who is
known as the father of graph theory. The origin of graph theory can be traced back to Euler's …

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are
discussed. A graph G is clique irreducible if every clique in G of size at least two, has an …

Given a graph G=(V, E), the Gallai graph of G, denoted by Γ (G), is the graph with vertex set
E in which two edges e and f of G are adjacent in Γ (G) iff e and f are adjacent in G but do not …

Abstract The Gallai graph Gal (G) of a graph G has the edges of G as its vertices, and two
distinct vertices e and f of Gal (G) are adjacent in Gal (G) if the edges e and f of G are …

Putting the concept of line graph in a more general setting, for a positive integer $ k $, the $ k
$-line graph $ L_k (G) $ of a graph $ G $ has the $ K_k $-subgraphs of $ G $ as its vertices …

Gallai graph of a graph G is a graph whose vertices are the edges of G and the adjacency of
the vertices depends on whether they are part of a triangle or not in G. We find some …