We consider a version of the on-line graph coloring problem as a two person game. Players are called Spoiler and Painter. Spoiler reveals a graph by putting or removing a node. But at each time the total number of nodes on the board is bounded by previously fixed constant n. Painter must assign a color to any new node such that two nodes connected by an edge have different colors. He cannot cha...

This paper considers a different version of the parallel machines scheduling problem in which the parallel jobs simultaneously requirea pre-specifiedjob-dependent number of machines when being processed.This relaxation departs from one of the classic scheduling assumptions. While the analytical conditions can be easily statedfor some simple models, a graph model approach is required when confli...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

The present study investigates the pendant number of certain graph classes; complement, line graphs, and total graphs. is minimum end vertices paths in a path decomposition graph. A it into subgraphs; i.e., sequence subset such that endpoints each edge appear one subsets vertex appears an adjacent sub-sequence subsets.

The Randić index of a graph G, denoted by R(G), is defined as the sum 1/d(u)d(v) for all edges uv where d(u) denotes degree vertex u in G. In this note, we show that R(L(T))>n4 any tree T order n≥3. A number relevant conjectures are proposed.

Fuzzy total chromatic number is the least value of k such that k-fuzzy coloring exist. In this paper, we discussed concept graphs to bistar graph and helm graph. Here define fuzzy Bistar Helm