Twin-distance-hereditary digraphs

Twin signed total Roman domatic numbers in digraphs

Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe conditions that (i) $sum_{xin N^-(v)}f(x)ge 1$ and$sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, where $N^-(v)$(resp. $N^+(v)$) consists of all in-neighbors (resp.out-neighbors) of $v$, and (...

Weakly Distance-regular Digraphs

Distance-two labelings of digraphs

For positive integers j ≥ k, an L(j, k)-labeling of a digraph D is a function f from V (D) into the set of nonnegative integers such that |f(x) − f(y)| ≥ j if x is adjacent to y in D and |f(x) − f(y)| ≥ k if x is of distant two to y in D. Elements of the image of f are called labels. The L(j, k)-labeling problem is to determine the ~λj,knumber ~λj,k(D) of a digraph D, which is the minimum of th...

(k, +)-Distance-Hereditary Graphs

In this work we introduce, characterize, and provide algorithmic results for (k, +)–distance-hereditary graphs, k ≥ 0. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k, +)–distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between the...

Probe Distance-Hereditary Graphs

A graph G = (V,E) is called a probe graph of graph class G if V can be partitioned into two sets P (probes) and N (nonprobes), where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. A graph is distance hereditary if the distance between any two vertices remains the same in every connected induced subgraph. Distancehereditary graph...