Let 𝐺 = (𝑉, 𝐸) be a connected graph. A locating-total dominating set in a graph 𝐺 is a total dominating set 𝑆 of a 𝐺, for every pair of vertices 𝑖, 𝑗∈ 𝑉(𝐺) \ 𝑆, such that 𝑁(𝑖) ∩𝑆 = ≠ ...

Look for the leftmost and rightmost points of the graph. If the graph extends indefinitely to the left or right, the domain includes negative or positive infinity, respectively. Note any breaks or ...

Graph distinguishing numbers constitute a vital parameter in understanding the symmetry properties of graphs. Fundamentally, the distinguishing number of a graph is the minimal number of labels ...

Cayley graphs provide a powerful and intuitive framework linking group theory with graph theory by representing groups through vertices and edges defined by a generating set. In the realm of finite ...

Carpathian Journal of Mathematics, Vol. 34, No. 2 (2018), pp. 143-155 (13 pages) In the paper, we extend known results concerning crossing numbers for join of graphs of order six. We give the crossing ...

Small separations in symmetric graphs (with B. Mohar) in preparation. Symmetric graphs with no K_n minor (with B. Mohar) in preparation Evolutionarily distinct species capture more phylogenetic ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c\) is a smooth curve with one turning point. The turning ...