Displaying similar documents to “The Crossing Numbers of Products of Path with Graphs of Order Six”

On path-quasar Ramsey numbers

Binlong Li, Bo Ning (2015)

Annales UMCS, Mathematica

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Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or Ḡ contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1,m), where Pn is a linear forest on m vertices. We determine the exact values of R(Pn,K1∨Fm) for the cases m ≤ n and m ≥ 2n, and...

Maximum Independent Sets in Direct Products of Cycles or Trees with Arbitrary Graphs

Tjaša Paj, Simon Špacapan (2015)

Discussiones Mathematicae Graph Theory

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The direct product of graphs G = (V (G),E(G)) and H = (V (H),E(H)) is the graph, denoted as G×H, with vertex set V (G×H) = V (G)×V (H), where vertices (x1, y1) and (x2, y2) are adjacent in G × H if x1x2 ∈ E(G) and y1y2 ∈ E(H). Let n be odd and m even. We prove that every maximum independent set in Pn×G, respectively Cm×G, is of the form (A×C)∪(B× D), where C and D are nonadjacent in G, and A∪B is the bipartition of Pn respectively Cm. We also give a characterization of maximum independent...

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Hossein-Zadeh, S., Hamzeh, A., Ashrafi, A. (2012)

Serdica Journal of Computing

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Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM...

Value-peaks of permutations.

Bouchard, Pierre, Chang, Hungyung, Ma, Jun, Yeh, Jean, Yeh, Yeong-Nan (2010)

The Electronic Journal of Combinatorics [electronic only]

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The Well-Covered Dimension Of Products Of Graphs

Isaac Birnbaum, Megan Kuneli, Robyn McDonald, Katherine Urabe, Oscar Vega (2014)

Discussiones Mathematicae Graph Theory

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We discuss how to find the well-covered dimension of a graph that is the Cartesian product of paths, cycles, complete graphs, and other simple graphs. Also, a bound for the well-covered dimension of Kn × G is found, provided that G has a largest greedy independent decomposition of length c < n. Formulae to find the well-covered dimension of graphs obtained by vertex blowups on a known graph, and to the lexicographic product of two known graphs are also given.

The Estrada Index

Hanyuan Deng, Slavko Radenković, Ivan Gutman (2009)

Zbornik Radova

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