Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is a drawing of the two graphs where each graph is drawn planar, no two edges overlap, and edges of one graph can cross edges of the other graph only at right angles. In the geometric version of the problem, vertices are drawn as points and edges as straight-line segments. It is known, however, that...

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to Kn (n ≥ 3), Km,n (m,n ≥ 2), and wheels Wr (r ≥ 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some speci...

The Strong Chromatic Index of Halin Graphs By Ziyu Hu A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they have adjacent endpoints. The strong chromatic index of a graph G, denoted by χs(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a planar graph constructed...

For any graph F and any integer r ≥ 2, the online vertex-Ramsey density of F and r, denoted m∗(F, r), is a parameter defined via a deterministic two-player Ramsey-type game (Painter vs. Builder). This parameter was introduced in a recent paper [arXiv:1103.5849 ], where it was shown that the online vertex-Ramsey density determines the threshold of a similar probabilistic one-player game (Painter...

The Firefighter Problem is a simplified model for the spread of a fire (or disease or computer virus) in a network. A fire breaks out at a vertex in a connected graph, and spreads to each of its unprotected neighbours over discrete time-steps. A firefighter protects one vertex in each round which is not yet burned. While maximizing the number of saved vertices usually requires a strategy on the...

A simple graphoidal cover of a semigraph is such that any two paths in have atmost one end vertex common. The minimum cardinality called the covering number and denoted by . acyclic an In this paper we find for wheel semigraph, unicycle zero-divisor graph.

Let f : V → {1, . . . , k} be a labeling of the vertices of a graph G = (V,E) and denote with f(N(v)) the sum of the labels of all vertices adjacent to v. The least value k for which a graph G admits a labeling satisfying f(N(u)) 6= f(N(v)) for all (u, v) ∈ E is called additive chromatic number of G and denoted η(G). It was first presented by Czerwiński, Grytczuk and Zelazny who also proposed a...

Let G∗ = (V, E) be a simple graph and A any nonempty set of parameters. subset R A×V an arbitrary relation from to V. mapping ᵖ(V) written as F:A → can defined F(x) { y ∈ V/xRy} ᵖ(E) K:A K(x) {uv E/{u, v} ⊆ F(x)}. The pair (F, A) is soft over V the (K, E. Obviously (F(a), K(a)) subgraph for all A. 4-tuple G ( G∗, F, K, called G. In this paper we discuss different graphs such Complete graph, Sta...

Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, γ(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are ...