Diberikan graf terhubung dan sederhana $G=(V(G), E(G))$ bilangan bulat positif $k$. Himpunan $S \subseteq V(G)$ disebut sebagai pembangkit $k$-metrik jika untuk setiap pasang titik berbeda $u,v \in V(G)$, terdapat paling sedikit $k$ $w_{1}, w_{2}, \ldots, w_{k} S$ sedemikian sehingga $d(u,w_{i}) \neq d(v,w_{i})$ $i \{1,2,\ldots, k\}$, dengan $d(u,v)$ adalah panjang \emph{path} terpendek dari $u...

We continue here the development of our description of the pullback approach to graph rewriting-already shown to encompass both the NCE and the double-pushout approach, by describing parallel application of rewriting rules. We show that this new framework provides a genuine deenition of parallel rewriting (parallel application of several rewriting rules at several diierent places in the graph i...

An injective map f : E(G) → {±1,±2, · · · ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f∗ : V (G) → Z − {0} defined by f∗(v) = ∑ e∈Ev f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f∗(V (G)) is either of the form { ±k1,±k2, · · · ,±k p 2 } or { ±k1,±k2, · · · ,±k p−1 2 } ∪ { ±k p+1 2 } according as ...

The traditional double-pushout approach to graph transformation does not allow to change node labels in an arbitrary context. We propose a simple solution to this problem, namely to use rules with partially labelled interface graphs and to match rules injectively. In [8] we have shown that injective matching makes the double-pushout approach more expressive, and here we further generalise that ...

An oriented walk double covering of a graph G is a set of oriented closed walks which, traversed successively, combined will have traced each edge of G once in each direction. A bidirectional double tracing of a graph G is an oriented walk double covering which consists of a single closed walk. A retracting in a closed walk is the immediate succession of an edge by its inverse. Every graph with...

Cai an Corneil (Discrete Math. 102 (1992) 103–106), proved that if a graph has a cycle double cover, then its line graph also has a cycle double cover, and that the validity of the cycle double cover conjecture on line graphs would imply the truth of the conjecture in general. In this note we investigate the conditions under which a graph G has a nowhere zero kow would imply that L(G), the line...

A connected graph G with chromatic number t is double-critical if G − x − y is (t − 2)-colorable for each edge xy ∈ E(G). The complete graphs are the only known examples of double-critical graphs. A long-standing conjecture of Erdős and Lovász from 1966, which is referred to as the Double-critical Graph Conjecture, states that there are no other double-critical graphs, i.e., if a graph G with c...