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11.341  Articles
1 of 1.135 pages  |  10  records  |  more records»
In this paper, the vertex-degree function index Hf(G) is considered when function f(x) belongs to four classes of functions determined by the following properties: strictly convex versus strictly concave and strictly increasing versus ... see more

We use Rosa-type labelings to decompose complete graphs into unicyclic, disconnected, bipartite graphs on nine edges – namely, those featuring cyclic component C4, C6, or C8. For any such graph H, we prove there exists an H-design... see more

The local antimagic labeling on a graph G with |V| vertices and |E| edges is defined to be an assignment f : E ? {1, 2, ?, |E|} so that the weights of any two adjacent vertices u and v are distinct, that is, w(u) ? w(v) where w(u) = Se ? E(u)f(e) and E(u)... see more

Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order n (? 6) and having locating-chromatic number n-3.

A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent vertices u and v in G.  The local metric dimension of G is the minimum cardinality of a local resolving set of G.  ... see more

Other than C9 there are 239 connected unicyclic graphs with exactly 9 edges. We use established graph labeling results to prove that every one of them decomposes the complete graph Kn if n = 0 or 1 (mod 18).

We use the subgraph replacement method to prove a simple product formula for the tilings of an  8-vertex counterpart of Propp's quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi... see more

In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2. Such graphs are cal... see more

Let G = (V, E) be a simple graph. A set  is a dominating set if every vertex in V(G) \ D is adjacent to a vertex of D. A dominating set D of a graph G is a complementary tree dominating set if induced sub graph (V \ D) is a tree. The domina... see more

1 of 1.135 pages  |  10  records  |  more records»