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Abstract: | Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied |
URI: | http://dyuthi.cusat.ac.in/purl/1534 |
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the edge C4 graph of a graph.PDF | (2.249Mb) |
Abstract: | We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed. |
URI: | http://dyuthi.cusat.ac.in/purl/1531 |
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Utilities Mathematica.PDF | (5.904Mb) |
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