Edge Neighbor Toughness of Graphs

Bounds of edge-neighbor-integrity of graphs

Let G be a graph. An edge subversion strategy of G is a set of edges T in G \vhose incident vertices are deleted from G. The survival-subgraph is denoted by G IT. The edge-neighbor-integrity of G. ENI( G). is defined to be ENI( G) = min {ITI + w'( G/T)}, where T is anv edge subversion strategv of G. and w'( G/T) T~E(G) • • is the maximum order of the components of G IT. In this paper. we find t...

Toughness and edge-toughness

Normalized Tenacity and Normalized Toughness of Graphs

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters.  Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.

Neighbor-distinguishing k-tuple edge-colorings of graphs

This paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum number of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.

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'...