Edge-Colored Graph Theory is a vibrant area within combinatorics that extends the classical study of graphs by assigning colours to edges. This paradigm not only uncovers subtle structural ...

If a graph is both **connected** *and* has no **cycles**, then it is **tree graph** [@benjamin17, p. 68]. The four tree graphs with five nodes are shown in @fig-trees. Recall from @sec-cycles in ...

The Yule tree graph The Yule tree is a graph with one edge coming in and two edges coming out of each branch-point. The branches represent the time periods between the evolution of new species. If the ...

AbstractFor a non-trivial connected graph 𝐺, a set 𝑆 ⊆ 𝑉 (𝐺) is called an edge geodetic set of 𝐺 if every edge of 𝐺 is contained in a geodesic joining some pair of vertices in 𝑆. The edge ...

The Yule tree graph The Yule tree is a graph with one edge coming in and two edges coming out of each branch-point. The branches represent the time periods between the evolution of new species. If the ...

The minimum edge-ranking spanning tree (MERST) problem on a graph is to find a spanning tree of G whose edge-ranking needs least number of ranks. Although polynomial-time algorithm to solve the ...

Edge-Colored Graph Theory is a vibrant area within combinatorics that extends the classical study of graphs by assigning colours to edges.