An injective map f : E(G) → {±1,±2, · · · ,±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f∗ : V (G) → Z − {0} defined by f∗(v) = ∑ e∈Ev f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f∗(V (G)) is either of the form { ±k1,±k2, · · · ,±k p 2 } or { ±k1,±k2, · · · ,±k p−1 2 } ∪ { ±k p+1 2 } according as ...

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5. Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph. For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic. In this way, we deal completely with 34 of these parameter se...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...

〈Summary〉 3D structure of proteins deeply relates to their functionality. It is wellknown that functions of proteins strongly appear in the bumpy parts of the molecular surfaces, and therefore geometric analysis of protein molecular surfaces is important. We propose a technique to extract geometric features of protein molecular surfaces, and a visual interface to effectively visualize the extra...

The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or, more generally, the complete k-partite graph. Lifting is a central tool to ...

Given a graph G = (V,E), an L(δ1, δ2, δ3)-labeling is a function f assigning to nodes of V colors from a set {0, 1, . . . , kf} such that |f(u) − f(v)| ≥ δi if u and v are at distance i in G. The aim of the L(δ1, δ2, δ3)-labeling problem consists of finding a coloring function f such that the value of kf is minimum. This minimum value is called λδ1,δ2,δ3(G). In this paper we study this problem ...

Using graph theoretic techniques, it is shown that the height characteristic of a triangular matrix A majorizes the dual sequence of the sequence of differences of maximal cardinalities of singular k-paths in the graph G(A) of A and that in the generic case the height characteristic is equal to that dual sequence. The results on matrices are also used to prove a graph theoretic result on the du...