Edge vulnerability parameters of bisplit graphs

Bisplit graphs

Vulnerability of super edge-connected graphs

A subset F of edges in a connected graph G is a h-extra edge-cut if G − F is disconnected and every component has more than h vertices. The h-extra edge-connectivity λ(G) of G is defined as the minimum cardinality over all h-extra edge-cuts of G. A graph G, if λ(G) exists, is super-λ if every minimum h-extra edge-cut of G isolates at least one connected subgraph of order h + 1. The persistence ...

Diameter vulnerability of graphs by edge deletion

Let f (t, k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-connected graph with diameter k. This paper shows 4 √ 2t−6 < f (t, 3) ≤ max{59, 5 √ 2t+7} for t ≥ 4, which corrects an improper result in [C. Peyrat, Diameter vulnerability of graphs, Discrete Appl. Math. 9 (3) (1984) 245–250] and also determines f (2, k) = 3k − 1 and f (3, k) = 4k − 2 for k ≥ 3. c © 2...

Domination parameters and edge-removal-critical graphs

For any of the basic domination parameters ir, , i, , or IR, we study graphs for which increases whenever an edge is removed ( -ER-critical graphs) and graphs for which decreases whenever an edge is removed ( −-ER-critical graphs). The latter case is only possible if = i or (perhaps) = ir. We give examples of classes of -ER-critical graphs for an upper domination parameter and characterize thes...

Edge-coloring Vertex-weightings of Graphs

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...