The Lovász θ function of a graph, a fundamental tool in combinatorial optimization and approximation algorithms, is computed by solving a SDP. In this paper we establish that the Lovász θ function is equivalent to a kernel learning problem related to one class SVM. This interesting connection opens up many opportunities bridging graph theoretic algorithms and machine learning. We show that ther...

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest a...

This papers deals with the Edge cordial labeling of newly introduced eight sprocket graph. graph is already proven as and gracious in labelling. In our study we have further proved that Eight Sprocket related families connected edge-cordial graphs. Also path union graph, cycle star are Edge-cordial.Â

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

Motivated by the conjecture on the L(2, 1)-labelling number λ(G) of a graph G by Griggs and Yeh [2] and the question: “Is the upper bound (∆+3)/4 for λ(G) for chordal graphs with maximum degree ∆ is sharp?”, posed by Sakai [3], we study the bounds for λ(G) for chordal graphs in this paper. Let G be a chordal graph on n vertices with maximum degree ∆ and maximum clique number ω. We improve the u...

A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several wel...

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...

Part of the authors introduced in [C. Huemer, S. Kappes, A binary labelling for plane Laman graphs and quadrangulations, in Proceedings of the 22nd European Workshop on Computational Geometry 83–86, 2006] a binary labeling for the angles of plane quadrangulations, similar to Schnyder labelings of the angles of plane triangulations since in both cases the labelings are equivalent to tree decompo...