(untitled) (Journal of Informatics and Mathematical Sciences, 2016)
This paper introduces the concepts of the \(m\)-clique load, the \(m\)-clique sequence and the \(m\)-clique density of graphs. The number of distinct maximum cliques over all maximal cliques is called the \(m\)-clique load of \(G\) and denoted, \((G)\). The \(m\)-clique sequence denoted, \(\)-sequence of a graph \(G\) with \(ε(G)1\) is the sequence with entries representing the number of maximal cliques of same order found in \(G\), in descending order. A finite sequence of positive integers each indexed with a distinct positive integer subscript which is \(c\)-graphical, is characterised. The \(m\)-clique density of a graph \(G\) denoted, \(p_c_i(G)\) is the probability of uniformly at random, choosing a maximal clique \(K_c_i\), \(1c_iu(G)\). Introductory results for certain graph classes and power graphs of balanced caterpillars, \(C^L_P_n\) are also presented.