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 ...

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

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 ...

The upper connected edge geodetic number g 1c + (G) is the maximum cardinality of a minimal connected edge geodetic set of 𝐺. Graphs 𝐺 of order 𝑝 for which g 1c (G)= g 1c + =p are characterized.

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 graph below shows the total number of publications each year in Binomial Edge Ideals And Graph Theory. References [1] Licci binomial edge ideals. Journal of Combinatorial Theory Series A (2020).

SIAM Journal on Applied Mathematics, Vol. 38, No. 3 (Jun., 1980), pp. 364-372 (9 pages) We prove that the edge dominating set problem for graphs is NP-complete even when restricted to planar or ...