The Independent Bondage Number of Planar Graphs Without Short Cycles

On 3-Distance Independent Sets of Graphs.

Let G be a graph with vertex set V(G) and edge set E(G). A set S \subseteq V(G) is a 3-distance independent set of G if d_G(v,w) \neq 3 for any two distinct vertices v,w \in S. The maximum cardinality of a 3-distance independent set of G, denoted by \alpha^3(G), is called the 3-distance independence number of G. In thi...

Theory & Applications of Graphs Theory & Applications of Graphs

This work establishes general properties of k -total bondage and finds exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.

2-Distance Certified Independence in the Join of Two Graphs

Acyclic (Δ + 2)-Edge Coloring of Toroidal Graphs Without Short Cycles

An acyclic edge coloring of a graph G is a proper edge coloring such that G contains no bichromatic cycles. The acyclic chromatic index χa′(G) is the minimum number of colors required for an acyclic edge coloring. Fiamčik and Alon et al. independently conjectured that χa′(G)≤Δ+2 for every simple graph G with maximum de...

Independent domination in central graphs

Let $G$ be a graph with vertex set $V(G)$. A set $I\subseteq V(G)$ is an independent dominating set of $G$ if no two vertices in $I$ are adjacent and every vertex in $V(G)\setminus I$ is adjacent to at least one vertex in $I$. The independent domination number of $G$ is the minimum cardinality among all independent dom...

isolate pendant domination number in semi-total point graphs and its application

Let G be a non-trivial graph. A dominating set I ⊂ V (G) is called an Isolate Pendant Dominating set (IPD-set) if the induced subgraph 〈I〉 has maximum degree at most one and contains at least one isolate vertex and at least one pendant vertex. The minimum cardinality of an IPD-set is called the IP domination number a...